MS 13. MAGIC SQUARES

DOUBLY MAGIC SQUARES:
Now I come to doubly magic squares: In these squares not only the basic square has the equisum property, but, if the numbers in each cell are replaced by their squares, the resultant square maintains the equisum property. Of course, in the new squares, the numbers will not be in sequence. I reproduce the 8x8 and 9x9 squares with these properties:
05 31 35 60 57 34 08 30
19 09 53 46 47 56 18 12
16 22 42 39 52 61 27 01
63 37 25 24 03 14 44 50
26 04 64 49 38 43 13 23
41 51 15 02 21 28 62 40
54 48 20 11 10 17 55 45
36 58 06 29 32 07 33 59

26 65 32 63 48 15 43 01 76
61 46 13 44 02 77 27 66 33
45 03 78 25 64 31 62 47 14
29 33 71 12 60 54 73 40 07
10 58 52 74 41 08 30 24 72
75 42 09 28 22 70 11 59 53
68 35 20 51 18 57 04 79 37
49 16 55 05 80 38 69 36 21
06 81 39 67 34 19 50 17 56
Here too from this one square a number of new squares can be generated. For example for the 8x8 square if we simultaneously interchange rows 1 & 2, and 7 & 8, and thereafter columns 1 & 2 and 7 & 8, we get the square:
09 19 53 46 47 56 12 18
31 05 35 60 57 34 30 08
22 16 42 39 52 61 01 27
37 63 25 24 03 14 50 44
04 26 64 49 38 43 23 13
51 41 15 02 21 28 40 62
58 36 06 29 32 07 59 33
48 54 20 11 10 17 45 55
It will be seen that combination of numbers in all rows, columns and diagonals is the same, so the resulting square will be doubly magic square. There are more such changes possible. In the case of 9x9 square besides such changes there are additional changes possible. For example 23+58+42=40+24+59, and their squares are also equal being 529+3364+1764=5657=1600+576+3481. Similarly 44+2+77=5+80+38, and their squares are also equal being 7869.

TREBLY MAGIC SQUARES:

It is possible to have magic squares where on replacement of numbers in each cell by the cube of the numbers the resultant square retains the equisum property, but, so far as it is known, we can have it only for the 128_128 square.

OTHER TYPES OF SQUARES;

I had stated that the Magic Squares must have, as one of the conditions, consecutive numbers. I now consider some other types of Squares which have the equisum property.

PRODUCT SQUARES:
We can, certainly, have squares where the sum of the products of the numbers in each row, column or diagonal is the same constant number. All we have to do is to write, instead of the numbers m,m+1,m+2,m+3...........: m,m^2,m^3............

SQUARES WITH ONLY ODD OR EVEN NUMBERS:
We can have squares which have only odd or even numbers in all the cells. Foe odd numbers square, all we have to do, is to increase all even numbers by n^2-1, and for all even number square merely increase all odd numbers by n^2+1, or simply double all the numbers in the cells.

OL 6. WISDOM IN ONE LINERS

You can't get rid of your temper by losing it?
Years wrinkle the skin, but to give up wrinkles the soul.
Work banishes three great evils - boredom, vice and poverty!
When it comes to shopping, some people have no shelf-control?
Want to see the bright side of your problems - talk to someone?
You can't depend on your judgment when your imagination is out of focus!
When you make a mountain of a molehill don't expect anyone to climb it!
What is beautiful is not always good, but what is good is always beautiful!
Without doubt it is a delightful harmony when doing and saying work together!
We should aim rather at leveling down our desires than at leveling up our means!

T10. WATCH

Let me now place a Thought for the day:
Watch your thoughts, they become your Mindset.
Watch your mindset, they become your Words.
Watch your words; they will govern your Behaviour.
Watch your behaviour, they become your Actions.
Watch your actions, they will evolve into a Pattern.
Watch these patterns, they will become your Habit.
Watch your habits,they will ultimately reflect your Character.
Watch your character, why?
They lay the path that your destiny will tread upon!!!!

FL25 - FL28. INTERSTING 4-LINERS

BE GOOD SWEET
Be good sweet, and who will be clever,
Do noble things, not dream all day long;
And so make life, death and that vast forever,
One grand sweet song!!!!!!

CONSPIRE
Ah Love! Could you and I with Him Conspire,
To grasp this sorry scheme of things entire,
Would not we shatter it to bits ~ and then
Remould it nearer to the heart's Desire.

ALL ALONE
As one who cons at evening o'er an album all alone,
And muses on the faces of the friends that he has known,
So I turn the leaves of 'fancy' till in shadowy design,
I figure the features of an old sweetheart of mine.

CHESS
I haven't played chess,
Since my funds got less,
My account is overdrawn,
And my pawns are in pawn!

A NICE TALE

A mother dropped a beautiful orange vase on the floor it splintered into dozens of pieces. She swept them up and threw them into the wastebasket.
An hour later she found her little daughter had collected the pieces and had pasted them on a piece of cardboard. Then using a green crayon, she had drawn stems and leaves on each piece, converting them into a bouquet of lovely flowers.
The mother was moved to tears. Where she had just seen trash, her daughter had seen a treasure.
And we? Do we see "treasures" in those around us? Are we willing to collect the bits and pieces of broken lives and bind them together again? Are we willing to take the trouble to make a lovely bouquet of flowers from the wastebasket of life.

DD26. DEFT DEFINITIONS

SAILOR A man who makes his living on a wave which he never touches on shore.
SAINT One who is in harmony with his creator.
SARCASM It is like a sword-stick, it appears at first sight to be much more innocent than it really is till, all of a sudden, there leaps something out of it, sharp and deadly, and incisive which makes you tremble and recoil.
SATAN The guide of those who refuse to be guided by others.
SATIRE 1) Art of stepping on somebody's toes.
2) Humour that has lost its patience.
SCANDAL A breeze whipped up by two or more wind -bags.
SCHOOL-WORK Something parent's ought to know.
SCIENCE 1) Topography of ignorance.
2) Systematic classification of expression.
SECRET An item of news which we pass on to our dear friends after taking a pledge from them that they will not disclose it to others forgetting that we ourselves had given a similarpledge.
SECRETARY The person behind the phone.
SELFISHNESS That detestable vice which no one will forgive in others and yet no one is without in himself.
SELF-PITY The most crippling handicap one can impose on oneself.
SENSUALITY Sister of infidelity.
SHAME An ornament to the young ; a disguise to the old.
SHOE An article of footwear which if tight, is a blessing in disguise, for it makes us forget all of our other troubles.
SICKNESS A belief which can be annihilated by the mind.
SILENCE A state which is said to be golden, but in the opinion of this lexicographer, if it does not involve tact it is not golden, for it is tact alone that gives it that quality.
SIMPLICITY A quality, which beyond a certain limit, leads to ruin.
SIN An action one who: Commits it is a man, Grieves at it is a saint, Boasteth of it is a devil.
SINCERITY A tree that takes a long time to grow and develop.
SLANDER A winged snake.
SLEEP 1) One normally gets it when it is time to get up.
2) Best cure for waking troubles.

MS 12. MAGIC SQUARES

TYPES OF SQUARES - BREAK-UP:
The split of the 880 squares by type as defined by us is:
Regular Squares - 528.
Type A - 120, 3 numbers <9 in one diagonal and 3 numbers >8 in the other.
Type B - 64, 2 numbers <9 and 2 numbers>8 in each row, column and diagonal, but not a Regular Square.
Type C - 120, all odd numbers in one diagonal and all even numbers in the other.
Type AB - 48, all odd numbers in one diagonal and all even numbers in the other, but otherwise Type A.

MAGIC SQUARES FROM MAGIC SQUARES:
We have seen earlier how we can construct a large number of squares of order 5 and above. We now discuss another special and interesting method for construction of 'p' order squares, where p = mxn, with both m and n being eaul to or greater yhan 3. The method requires that we replace the integers by the squares of of the other order. We illustrate this method for the 12x12 square, 12 being equal to 3x4.
The 12x12 square will have 144 cells, numbers to be used will be from 1 to 144, and the magic sum will be 145x6=870. Imagine these 144 cells being divided into 9 compartments having 16 adjacent cells in 4 rows and 4 columns. If we allot to the compartment numbers from 1 to 9 as if we are constructing a 3x3 square, all we need to do is to replace these numbers 1 to 9 by 4x4 squares. This is what we have to do:
1 is to be replaced by 4x4 square with numbers from 1 to 16 and total 34.
2 is to " " " " " 17 to 32 and total 64+34=98.
3 is to " " " " " 33 to 48 and total 128+34=162.
......................................... 9 is from 129 to 144, total 512+34= 546.
Now in the 3x3 square one set of diagonal is 4,5&6, so we get the for the mail diagonal a total of 192+34+256+34+320+34= 870, the required total for a 12x12 square. All numbers from 1 to 144 have been used once only etc. While there is only one solution for the 3x3 square (the square however can be rotated) there are 880 choices for each of the 9 squares we have to use, and since all of them can be rotated we have in all 880x4^9 squares that can be obtained, each different.
Alternately we divide the 144 cells into 16 compartments numbering from 1 to 16, forming the 4x4 square, all we have to do now is replace 1 by a 3x3 square with numbers from 1 to 9, 2 by a 3x3 square with numbers from 10 to18, and so on...
As we can use 880 squares for the 4x4 square we have 880x4^16 squares. Of course, for odd number squares the Hindu Rule is always there and for singly even order squares the border square method.

MORE ABOUT 8X8 SQUARE:
Before we proceed further note that there are exceptions. The 8x8 square can be constructed with the help of 4x4 squares. This is possible because the total required is 260, and so if we have 4 compartments of 4x4 squares each having a total of 130, we get the 8x8 squarte. The only restriction here would be that we cannot use all the 880 squares but 712 squares. (We cannot use squares of Type A and Type AB for obvious reasons).

MORE ABOUT 12X12 SQUARES:
In the same manner we can also construct 12x12 squares from 6x6 squares, provided we construct the 6x6 squares by De La Hire's method. The 4 squares required are to be formed by adding:
0 to numbers from 1 to 18 and 108 to numbers from 19 to 36.
18 to " 1 to 18 and 90 to " from 19 to 36.
36 to " 1 to 18 and 72 to " from 19 to 36.
54 to all numbers.
Note: For the last square all the 880 squares can be used as the same number 54 is being added to all numbers.
We can similarly form other squares also with due precaution of selecting the right squares.

A15. YOU WILL ENJOY READING THIS TALE

A kindergarten (KG school) teacher has decided to let her class play a game.
The teacher told each child in the class to bring along a plastic Bag containing a few potatoes. Each potato will be given a name of a person that the child hates, so the number of potatoes that a child will put in his/her plastic bag will depend on the number of people he/she hates. So when the day came, every child brought some potatoes with the name of the people he/she hated. Some had 2 potatoes; some 3 while some up to 5 potatoes.
The teacher then told the children to carry with them the potatoes in the plastic bag wherever they go (even to the toilet) for 1 week. Days after days passed by, and the children started to complain due to the unpleasant smell let out by the rotten potatoes. Besides, those having 5 potatoes also had to carry heavier bags. After 1 week, the children were relieved because the game had finally ended.
The teacher asked: "How did you feel while carrying the potatoes with you for 1 week?" The children let out their frustrations and started complaining of the trouble that they had to go through having to carry the heavy and smelly potatoes wherever they go. Then the teacher told them the hidden meaning behind the game. The teacher said: "This is exactly the situation when you carry your hatred for somebody inside your heart.
The stench of hatred will contaminate your heart and you will carry it with you wherever you go. If you cannot tolerate the smell of rotten potatoes for just 1 week, can you imagine what is it like to have the stench of hatred in your heart for your lifetime?"
Moral of the Story:
Throw away any hatred for anyone from your heart so that you will not carry sins for a lifetime. Forgiving others is the best attitude to take. "Learn to Forgive and Forget."

A14. A LOOK AT THE ENGLISH LANGUAGE

Let's face it - English is a crazy language.
1) There is no egg in eggplant nor ham in hamburger. Neither apple nor pine in pineapple.
2) English muffins weren't invented in England nor French fries in France
3) Sweetmeats are candies while sweetbreads, which aren't sweet, are meat.
4) We take English for granted. But if we explore its paradoxes, we find that quicksand can work slowly, boxing rings are square and a guinea pig is neither from Guinea nor is it a pig.
5) And why is it that writers write but fingers don't fing; grocers don't groce; and hammers don't ham?
6) If the plural of tooth is teeth, why isn't the plural of booth beeth?
One goose, 2 geese. So one moose, 2 meese? One index, 2 indices?
7) Doesn't it seem crazy that you can make amends but not one amend.
8) If you have a bunch of odds and ends and get rid of all but one of
them, what do you call it?
9) If teachers taught why didn't preachers praught?
10) If a vegetarian eats vegetables, are humanitarians cannibals?
11) In what language do people recite a play and play at a recital?
12) Ship by truck and send cargo by ship?
13) Have noses that run and feet that smell?
14) How can a slim chance and a fat chance be the same, while a wise man and a wise guy are opposites?
P.S. Why doesn't Buick rhyme with quick?

DD25. DEFT DEFINITIONS

QUALITY a) The best is cheapest.
b) Signature of excellence.
QUOTATIONS Short sentences based on long experience.
REACTIONARY A somnambulist walking backwards.
REALITY Not what you feel, but how you feel.
REASON a) Every why hath a wherefore.
b) A cold arithmetician summing up our follies.
REBELLION Medicine necessary for the sound health of the government.
REGRET It might have been !
REJUVENATION One step backwards in order to take a better leap.
RELATIVITY That hour, which when you are courting a nice girl, seems like a second, while on the other hand, when you sit on a red-hot cinder, it is the second that seems like an hour.
RELIGION a) Opium of the people.
b) Tries to explain the nature of the unknowable.
c) Root cause of all serious conflicts.
d) A daughter of hope and fear explaining to the ignorant the nature of the unknowable.
e) Something men wrangle about, write about, fight about, die for, do anything but live it.
REMEMBERANCE A form of meeting.
REPENTANCE Promise made and kept to do something no more.
REPUTATION An enviable possession so long has one does not have to live up to it.
RESEARCHER He sees what everyone sees, but he thinks what none of us thought.
RESPECT A state of mind forced upon children by their parents, it becomes a habit, in due course of time, and sticks.
REVOLUTION A successful effort to get rid of an existing bad government and its replacement by a worse one.
RHETORIC Art of ruling the minds of men.
RIDICULE Evidence of wit or bitterness which gratifies a little mind or an ungenerous temper but is no test of reason or truth.
RING (WEDDING) The smallest hand-cuffs known to homo-sapiens and generally willingly É..
RITUALS Some tangible thing that adds beauty to worship and bears testimony to splendour and the majesty of God.
ROBOT An industrial worker with a lot of brain but without intelligence.
ROMANCE a) Dance-tune.
b) Romance is to love what a picnic is to the business of eating.
RUDENESS Weak man's imitation of strength.

MS11. MAGIC SQUARES

ORDER 4 MAGIC SQUARES - ALL 880 SQUARES.
Coming back to order 4 squares, we examine them is detail as there are only 880 solutions.
When can we not have them?
First point to be noted is that the sum of all odd numbers between 1 & 16 is 64 and all even numbers is 72. Since the magic sum figure is 34 (an even number), each row or column or diagonal will have either 2 or 4 odd numbers. But if we have odd numbers only in one row (or column), the other row (or column) will necessarily have only all odd numbers and we will fail to get the magic sum. However, one diagonal can only have odd numbers provided the other diagonal has only even numbers.
Similarly we cannot have a square if sum of the corner numbers does not add up to 34. The sum of the corner numbers has to be 34 only, not more nor less.
We also cannot have only odd (or even) numbers in corners, since if we have odd (or even) numbers in the corners, all middle numbers will have to be even (or odd) numbers, and including diagonal numbers it makes for 12 numbers, while we have only 8 even and 8 odd numbers. And if we take only odd numbers in both diagonals again we cannot get the magic sum.

RULES FOR FORMATION
Now let us examine the Rules that will enable us to generate more squares from already generated square (may be by trial and error or by the auxiliary square method). Let us for this purpose, represent the magic square as seen below:
a b c d
e f g h
i j k l
m n o p
Rule 1. For all types of squares we get a new square by simultaneously changing
b&c, h&l, n&o, e&i f&k, g&j.
Rule 2. Change inner numbers f,g,j,k to corner numbers a,d,m,p and corners numbers to places occupied by f,g,j,k, but otherwise retaining the numbers of the rows and columns.
Rule 3. Change all even numbers to odd numbers by decreasing by 1, and odd numbers to even by increasing them by 1.
Rule 4. Subtract all numbers from n^2+1 = 17.
Rule 5. If f+k = g+j = 17, we can inter-change the middle rows or columns, both can be inter-changed but not necessary in view of Rule 1.
Rule 6. If b+c = either f+g or j+k and n+o = the remaining of f+g or j+k and f+k = b+o or b+n we can inter-change b,c & n,o with f,g &j,k. Same holds good for e,i & h,l.
Rule7. If e+h = 17 and i+l =17, we can inter-change e,h& i,l. Same is true for b,n & c,o. Or if e+i = h+l = 17, we can replace h,l by e,i, and vice-versa. Same holds good for b,n & c,o.
(It will be seen that some of these rules will not be valid for some of the squares. In particular Rule 3 will not be valid for a square, which has only odd numbers and even numbers in its diagonals. Rule 4 may not produce a new square if corner numbers are complementary, i.e. add up to 17 in pairs).
Rule 8. Applicable to only Regular Squares which number 528 in all. Change diagonal a,f,k,p to first row and m,j,g,d to 4th row and rewrite the numbers between a to m & d to p. Similarly change diagonals to columns and vice-versa to get a new square.

Now let us see how these rules work for a particular square. We start with the Main square shown below:
01 12 14 07
06 15 09 04
11 02 08 13
16 05 03 10
Rule 7 will give 3 more squares as shown below:
01 12 14 07 - - 01 14 12 07 - - 01 14 12 07
04 15 09 06 - - 06 15 09 04 - - 04 15 09 06
13 02 08 11 - - 11 02 08 13 - - 13 02 08 11
16 05 03 10 - - 16 03 05 10 - - 16 03 05 10
If we now apply Rule 1 to all these squares we get 4 more squares:
01 14 12 07 - - 01 14 12 07 - - 01 12 14 07 - - 01 12 14 07
11 08 02 13 - - 13 08 02 11 - - 11 08 02 13 - - 13 08 02 11
06 09 15 04 - - 04 09 15 06 - - 06 09 15 04 - - 04 09 15 06
16 03 05 10 - - 16 03 05 10 - - 16 05 03 10 - - 16 05 03 10
Now we apply Rule 8 to the main square to generate 2 more squares.
01 15 08 10 - - 01 12 14 07
06 12 03 13 - - 15 06 04 09
11 05 14 04 - - 08 13 11 02
16 02 09 07 - - 10 03 05 16
Rule 7 applied to the left-hand side square along with Rule 1, will give 8 new squares. Rule 5 applied to the right-hand square along with Rule 1 will give 4 new squares. In all, as such, we get in all 20 squares.
Now applying Rule 3 to the main square we get:
02 11 13 08
05 16 10 03
12 01 07 14
15 06 04 09
When we apply Rules 1, 5, 7 & 8 we get additional 19 squares or in all 20 squares.
Also let us apply Rule 2 to the left-hand side square and then Rule3 to the newly generated square and see what happens. We get the following 2 squares:
06 15 09 04 - - 05 16 10 03
12 01 07 14 - - 11 02 08 13
03 10 16 05 - - 04 09 15 06
13 08 02 11 - - 14 07 01 12
These 2 will also generate 19 additional squares, giving us in all 40 squares.
So from 1 main square and applying the various Rules we have been successful in getting 79 additional squares!!!!!!

REGULAR SQUARES
For Rule 8 we talked of Regular Squares - so what is a Regular square? If we reduce all numbers from 1 to 16 by 1, we get numbers from 1 to 15, and it will be noticed that all these numbers are a combination of 1, 2, 4 & 8. Let us now place the numbers from 0 to 15 in a 4x4 square to give a total of 30 for all its rows, columns and 2 main diagonals. Now if we split the numbers of this modified square into its components of 12, 2, 4 & 8 and place them in separate 4x4 squares, and the squares get so formed that none of the numbers 1, 2, 4 & 8, occur more than twice in any row, column or diagonal in their respective squares, we get what is called a Regular Square. Let us try this for the main square discussed earlier. Reducing all numbers by 1 we get the square:
00 11 13 06
05 14 08 03
10 01 07 12
15 04 02 09
And the split numbers get arranged in the squares as under:
X 1 1 x - - x 2 x 2 - - x x 4 4 - - x 8 8 x
1 x x 1 - - x 2 x 2 - - 4 4 x x - - x 8 8 x
x 1 1 x - - 2 x 2 x - - x x 4 4 - - 8 x x 8
1 x x 1 - - 2 x 2 x - - 4 4 x x - - 8 x x 8
(x has been placed to fill up blank spaces.)
It will be noticed that the numbers fall in the pattern required for a Regular Square.
If we, however, examine the square reproduced below it will be found that it is not a Regular Square:
01 10 15 08
05 14 11 04
16 03 06 09
12 07 02 13

G6. BIRTHDAY WISHES

Like the fresh drops of morning dew,
People like you are both rare and few.
Like all those who are generous and kind,
You rate among those who are hard to find.
So, go ahead and celebrate in a special way,
Just the way you like with all our GOOD WISHES.

WORDS NEEDING ATTENTION - 5.

COURAGE - Courage is finding the inner strength and bravery required when confronting danger, difficulty or opposition. Courage is the energy current behind all great actions and the spark that ignites the initial baby steps of growth. It resides deep within each of us, ready to be accessed in those moments when you need to forge ahead to break through seemingly insurmountable barriers.

DIFFICULT TIMES - Sometimes, when we are at a difficult time in our lives, we do not reach out for help. Maybe it is because we are proud, maybe we think we would be bothering someone with out troubles. Perhaps we are embarrassed. Or we might think that what is troubling us has never bothered anyone before and we are afraid to show our fears or feelings. Is it correct? We should learn to share our miseries, in a tactful manner, just as we would like others to share our joys, and take guidance.

A13. MAYBE THIS IS WHY THE ENGLISH LANGUAGE IS SO HARD TO MASTER.

1) The bandage was wound around the wound.
2) The farm was used to produce, produce.
3) The dump was so full that it had to refuse more refuse.
4) We must polish the Polish furniture.
5) He could lead if he would get the lead out.
6) The soldier decided to desert his dessert in the desert.
7) Since there is no time like the present, he thought it was time to present the present.
8) A bass was painted on the head of the bass drum.
9) When shot at, the dove dove into the bushes.
10) I did not object to the object.
11) The insurance was invalid for the invalid.
12) There was a row among the oarsmen about how to row.
13) They were too close to the door to close it.
14) The buck does funny things when the does are present.
15) A seamstress and a sewer fell down into a sewer line.
16) To help with planting, the farmer taught his sow to sow.
17) The wind was too strong to wind the sail.
18) After a number of injections my jaw got number.
19) Upon seeing the tear in the painting I shed a tear.
20) I had to subject the subject to a series of tests.
21) How can I intimate this to my most intimate friend?
22) We bank upon bank for safety of our savings.
23) The king's court framed many rules but the king simply ruled ignoring the rules.

DD24. DEFT DEFINITIONS.

a) PRAISE Sweetest of all sounds.
b) A bitter pill. Only a few people can swallow it.
c) In relationship to oneself must be done daringly. Something will always stick
PRAYER A wish turned heavenward.
OM work.
PREACHER One who cannot do.
PREJUDICE a) A mist, which in our journey through the world, often dims the brightest and obscures the best of all the good and glorious objects that meet us on our way.
b) A device that enables you to form opinions without getting the facts.
PRIDE a) The only thing a women in love cannot keep.
b) A ridiculous encumbrance.
PRINCIPLE A passion for truth and right ?
PROCRASTINATION a) Thief of our self-respect.
b) Opportunity's natural assassin.
PROGRESS Exchange of one nuisance for another one .
PROMISE Resolve made to be broken.
PROPHETS Men whose forecasts, if right ,no one remembers and, if wrong, no one forgets.
PROSE Words in their best order.
PROVERB a) A short sentence based on long experience.
b) Creation of wise men repeated by fools.
Psychologist a) A person who observes us when we are looking at girls in the swimming pool.
b) A man who, when a beautiful girl enters the room, watches everyone else.
Psychiatrist is a man who pockets your money for dismantling your dreams
PUBLIC A spoilt child.
PUBLIC-OFFICE First refuge of the incompetent.
PUBLIC-OPINION A vulgar, impertinent, anonymous tyrant who deliberately makes life unpleasant for anyone who is not content to be an average man.
PUN Lowest form of humour when you don't think of it first.
PUNISHMENT Eye for eye, tooth for tooth, hand for hand and foot for foot.
PURITY A noble perception which, like virginity, must be violated if life is to persist.

WORDS NEEDING ATTENTION - 4

BLESSINGS - I am a confirmed believer in 'blessings in disguise'. I prefer them undisguised when I happen to be the person blessed. But the theory that blessings in disguise are constantly happening to other people I find consoling. It enables me to bear their troubles without feeling miserable.

CHARACTER - The most authentic witnesses of our character are those who know us in our family and see us without any restraint or rule but such as we voluntarily prescribe for ourselves.

CHILDREN - God has sent children to enlarge our hearts and to make us unselfish and full of kindly sympathies and affections rather than merely to keep up the race. - Children assist us in more ways than one: to give our souls higher aims; to call out all our faculties: to extended enterprise and exertion; and to sing round our firesides - bright faces, happy smiles and loving tender hearts.

CONTENTMENT - The fountain of contentment must spring up in the mind, and he who has so little knowledge of human nature as to see happiness by changing anything but his own disposition will waste his life in fruitless efforts and multiply the grief's which he proposes to remove.

DD23. DEFT DEFINITIONS

PLAGIARISM The unoriginal sin.
PLATITUDE Simple truth repeated till people get tired of hearing it.
PLEASURE Fruit of a tree called toil.
POET A sick soul of society.
Bad, mad, glad, sad, human being.
POETRY Best words in the best order.
Expression of imagination.
Painting with the gift of speech.
Record of the best and the happiest moments of the best and the happiest minds.
A perfume which on evaporation leaves in our soul the essence of beauty. 6.Men's thoughts tinged by his own feelings.
POLITENESS It is like an air-cushion, there may be nothing in it, but, it eases our joints wonderfully.
POLITICIAN A necessary evil in democracy.
POLITICS Science of exigencies.
POPULACE Contemporary of blotters. They soak it all in but get them backwards.
POPULARITY A crime from the moment it is sought.
Avirtue when men have it whether they will it or not.
POST A strange volume of real life in the daily pocket of a post-man.
POVERTY Violence against humanity.
POWER Iron hand in a velvet glove.

WORDS NEEDING ATTENTION - 3.

AMBITION - The passion of ambition is the same in a courtier, a soldier or an ecclesiastic; but from their different educations and habits they will take very different methods in gratifying it.

AWE- Out of our recognition in fear and awe that there is an unknowable comes all that is best in the exploration of the mind, even though that recognition often misleads us into superstition, enslavement and over-confidence.

BENDING - The exercise most frequently performed by human beings. We bend over backwards for some people; we bend low fawning over others; we never miss a bender; teachers give benders; we periodically bend to pick up the shattered pieces of our lives; we bend double with pain; we bend low with care; we bend to touch our toes in vain attempt to stave off the middle age spread. In fact we are now beginning to stoop to any lengths.... And I wonder why our forefathers ever bothered to stand up in the first place.

FL22-FL25. INTERESTING 4-LINERS.

WEEP ON
Weep on - perhaps in after days,
They will learn to love your name,
And many a deed may wake in praise.
That long hath slept in blame.

WISE OLD BIRD
A wise old bird sat on an oak.
The more he heard, the less he spoke;
The less he spoke, the more he heard;
Let us not laugh at this wise old bird.

WORDS
I'm careful of the words I say
To keep them soft and sweet;
For I know not from day to day
Which one's I'll have to eat.

WORRYING
What's the use of worrying?
It never was worthwhile,
So pack up your troubles in your old kit bag,
And smile, smile and SMILE!

T9. MISMANAGEMENT PROCESS

A story is told about 4 people named Everybody, Somebody, Anybody and Nobody. There was an important job to be done and Everybody was sure that Somebody would do it. Anybody could have done it, but Nobody did it. Somebody got angry about that, because it was Everybody's job. Everybody thought Anybody could do it. But Nobody realized that Everybody would not do it. It ended up that Everybody blamed Somebody when Nobody did what Anybody could have done.
How management in a missionary institution is so different from others?
There, Nobody is irresponsible. Everybody would give the best. Somebody even excels. Anybody does the job willingly with a spirit of devotion to duty.

MS10. MAGIC SQUARES

SUMMING UP:

We have seen that a 3x3 square only one and 4x4 square 880 solutions and can be constructed by the auxiliary method and also by other methods. A 5x5 square can be constructed either by the Hindu Rule which gives 720 squares from one set, or by the Border Square method with the 3x3 square as the base, or from two auxiliary squares which at once gives 3,600 squares from one set. Further 5x5 squares can be constructed by either constructing 3x3 squares with total of 39 with 13 in the central cell, or by first forming a 3x3 square with any number in the central cell and thereafter filling up the remaining cells with numbers of our choice, except that the total for any one row or column or diagonal should not be more than62. Some illustrations are given below, first 2 with 13 in the central cell:
22 18 10 09 06
07 12 03 24 19
11 25 13 01 15
05 02 23 14 21
20 08 16 17 04

20 01 23 09 12
22 08 21 10 04
02 15 13 11 24
07 16 05 18 19
14 25 03 17 06
Now with 15 in the central cell and different totals for rows and columns for the 3x3 square:
01 10 19 23 12
09 18 22 11 05
17 21 15 04 08
25 14 03 07 16
13 02 06 20 24
It will be seen that the numbers in the border square do not follow any pattern. But we can form additional squares by subtracting all numbers from 26._As is the case with 4x4 square, for 5x5 square too, we can frame rules which will enable us to generate squares from the one already constructed. Let the square be represented by:
a b c d e
f g h i j
k l m n o
p q r s t
u v w x y
We can now generate new squares by interchanging any two columns or rows provided this does not affect the diagonal totals, some examples are given below:
a) If g+s = i+q, we can interchange 2nd and 4th columns
b) If h+n = m+i and m+s=r+n, 3rd and 4th columns.
c) If g+m=h+l and h+n=i+m, 2nd and 3rd rows.
d) If g+m=h+l and l+r=m+q, 2nd and 3rd columns.
e) If l+r=m+q and m+s=r+n, 3rd and 4th rowsw.
f) Also if b+c=v+w, they can be interchanged in the 1st and 5th rows, etc.
g) As stated earlier new squares can be generated merely by subtracting all numbers from 26. These rules, incidentally, have applicability in general for all squares of any order.

A12. "I"

It starts with "I". Well you see my body, but this is a superficial view. In addition to my body there is another component which enables me to feel joy and sorrow. This part of me is the "Mind". Moving a little deeper, I find another part of me, which enables me to control my Mind - that is "Intellect". Looking further when I'm awake, I see the "Universe" around me, but what happens when I am asleep? I am unaware of what is happening around me. But in my dream I may feel and see some things! Is the "Dreamer" different from the "Waker". It appears that "I" am in a different world when "I" am awake from the one "I" inhabit during my sleep. The Vedas examine whether there is only one world, which "I" see in my waking state or more than one world. It is this "I" to which the name "Awareness" or "Consciousness" is given. The Vedas call it "Atma" or "Soul". In the vast literature on Indian Philosophy and in the Upanishads, where the nature of Atma is explored, it is described as "Self". A closer look indicates that all existence is the interplay of "Consciousness", "Action" and "Matter" or else interplay of "Mind", "Matter" and "Motion" or worded slightly differently as the interaction of "Knowledge", "Objects" and "Process".
An Object occupies "Space", whereas Awareness does not. This brings us to the hot question - like the one that Hen came first or the Egg, whether Awareness or Consciousness came first or Existence? There are three aspects - that of Seeing or Observing, that of being Seen or Observed and that of the One who is Observing the Object which is Seen. It is difficult to decide the sequence of Awareness and Existence, because Awareness of an object is proof of its Existence, but the fact that we are not Aware of a Thing does not mean that it does not Exist. That is where FAITH comes in! And FAITH is the substance of things hoped for and evidence of things not seen, isn't it so?

MS9. MAGIC SQUARES

Other Methods:
We conclude this part with a few methods which are more of academic interest as they yield one or just a few squares. Cosider the picture below (dashes have been used to fill up empty spaces):
- - - - - - - - 01 - - - - - - - -
- - - - - - - 06 - 02 - - - - - - -
- - - - - - 11 - 07 - 03 - - - - - -
- - - - - 16 - 12 - 08 - 04 - - - - -
- - - - 21 - 17 - 13 - 09 - 05 - - - -
- - - - - -22 - 18 - 14 - 10 - - - - -
- - - - - - - 23 - 19 - 15 - - - - - -
- - - - - - - - 24 - 20 - - - - - - -
- - - - - - - - - 25 - - - - - - - - -
Now we have to simply move the numbers, which are outside the main square, 5
steps to the empty spaces to get the following 5x5 square.
11 24 07 20 03
04 12 25 08 16
17 05 13 21 09
10 18 01 14 22
23 06 19 02 15
This method is attributed to Bachet de Meziriac. Same principle holds good for constuction of higher order odd squares. We now have a look at a 6x6 square. Write numbers from 1 to 36 in their natural order as shown below:
01 02 03 04 05 06
07 08 09 10 11 12
13 14 15 16 17 18
19 20 21 22 23 24
25 26 27 28 29 30
31 32 33 34 35 36
Replace 2,3,4,5 by 35,34,3,32 respectively; 7 & 25 by 30 & 12; 13 & 19 by 24 & 13; 9 & 10 by 28 & 27; 12 & 30 by 7 & 25; 18 & 24 by 19 & 18; 17 & 23 by 14 & 20; 27 & 28 by 9 & 10; 32, 3, 34, 35 by 2, 4, 33, 5 respectively, giving a 6x6 square as under:
01 35 34 03 32 06
30 08 28 27 11 07
24 23 15 16 14 19
13 17 21 22 20 18
12 26 09 10 29 25
31 02 04 33 05 36
Note that diagonal numbers were not changed. Since 6/2 is odd a 6x6 square needs quite a few changes making it cumbersome, however, it is easier to construct a 8x8 square this way. Write the numbers 1 to 64 in their natural order as shown below:
01 02 03 04 05 06 07 08
09 10 11 12 13 14 15 16
17 18 19 20 21 22 23 24
25 26 27 28 29 30 31 32
33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48
49 50 51 52 53 54 55 56
57 58 59 60 61 62 63 64_
Now divide by 2 vertical and 2 horizontal lines so that in each corner there is a 2x2 square and in the center a 4x4 square. Within these 5 squares inter-change all pairs of numbers symmetrically opposite. Outside the 5 squares no change is required. The resulting square will thus be as under:
64 63 03 04 05 06 58 57
56 55 11 12 13 14 50 49
17 18 46 45 44 43 23 24
25 26 38 37 36 35 31 32
33 34 30 29 28 27 39 40
41 42 22 21 20 19 47 48
16 15 51 52 53 54 10 09
08 07 59 60 61 62 02 01
Well we can go the other way round too. Keep the 4 corner 2x2 squares and the central 4x4 square as they are and reverse the other 4x2 squares in rows 3, 4, 5 & 6 and columns 1 & 2 and 7 & 8 and the rows 1 & 2 and 7 & 8 in columns 3, 4, 5 & 6 to form the new square. I will illustrate this by 12x12 cell, but before that please note that this method is valid for all squares which are multiples of 4. So if the square is 4nx4n, we take the corner cells of the order nxn and the central cell of the order 2nx2n for reversal. Alternately we retain the 4 corner nxn squares and central 2nx2n squares unchanged and reverse the squares, as seen below for the 12x12 square.
001 002 003 141 140 139 138 137 136 010 011 012
013 014 015 129 128 127 126 125 124 022 023 024
025 026 027 117 116 115 114 113 112 034 035 036
108 107 106 040 041 042 043 044 045 099 098 097
096 095 094 052 053 054 055 056 057 087 086 085
084 083 082 064 065 066 067 068 069 075 074 073
072 071 070 076 077 078 079 080 081 063 062 061
060 059 058 088 089 090 091 092 093 051 050 049
048 047 046 100 101 102 103 104 105 039 038 037
109 110 111 033 032 031 030 029 028 118 119 120
121 122 123 021 020 019 018 017 016 130 131 132
133 134 135 009 008 007 006 005 004 142 143 144
It will be noticed that here too we can generate a large number of squares very easily. It will be noticed that pairs of numbers have same total, which can be interchanged without affecting the diagonal totals. A few examples:2+95=3+94, 2+83=3+82, 84+109=85+110, etc. More, work out yourself. It will also be seen that it can be done in 8x8 square too.

OL5. WISDOM IN ONE LINERS

Where boasting ends dignity begins.
You can plant anything in an open mind.
Vice is the darkness that brings virtue to light.
When your work speaks for itself, don't interfere!
There's no hardship more crippling than self-pity!
Virtue alone is the unerring sign of a noble soul!
Trouble is an ounce or a ton depending on how we take it?
The first rule for speaking well, naturally, is to think well!
The world is a beautiful book but what use to him who cannot read?
The drama is make-believe art, it does not deal with truth but with effect.
The only conquests that cause no regrets or envy are those made over ignorance?

DD22. DEFT DEFINITIONS

DD22. PALMIhttp://www.blogger.com/img/gl.link.gifST An ignorant man who takes counsel from stars instead of from God who made the stars.
PAIN A strong feeling that at times forces even an innocent to lie.
PAINTING Silent poetry.
PAPER It is the God of bureaucracy, just as the Sun is for other people. The babus who join ink-stained hands in prayer to the processed celluloid sometimes display a faith so blind that it is sublime.
PARKING-SPACE An area of about 7'x14' on the other side of the road.
PARTING A sweet sorrow, but take note that journey's end in lover's meetings.
PASSIONS Certain qualities in human behaviour which are not well looked at. To be frank they are the winds that fill the sails of a vessel. They sink it at times but without them it would be impossible to make way. Many things that are dangerous here below are, all the same, necessary.
PAST a) A bucket of ashes.
b) Best prophet of future.
c) Pathology is the science of a disease called "inquiries"
PATIENCE a) The fine art of hoping.
b) An ornament to a woman and modesty to a girl.
c) The key for contentment.
d) An appropriate strategy that is often overlooked on important occasions.
PATRIOTISM The last refuge of a scoundrel.
PEACE A monotonous interval between two wars or disastrous fights.
PEN Tongue of the mind.
PERSEVERANCE The courage to hold on when all others have given up.
PESSIMIST Who rejoices in proving that there is no joy.
PHILOSOPHER A lunatic who can analyze his delusions.
PHILOSOPHY a) Old hag's description of the menu in paradise.
b) Unintelligible answers to insoluble problems.
c) A route of many roads leading from nowhere to nothing.
d) The account which the mind gives to itself of the constitution of the world.
PICTURE Poem without words.
PITY A cheap gift which could have no weight at all either for good or bad but can do a lot of damage.It accentuates troubles that would be less painful if the sufferer is not reminded of them.

G5. BIRTHDAY GREETINGS

Listen to the echo within your heart,
If it beats with hope today.
It means you celebrate some years well lived,
On this yet another birthday,
Follow the sound with eyes well closed.
Trust yourself in its fold,
For it says the silver years of your life
Will soon turn into Gold!!!!!

WORDS NEEDING ATTENTION - 2.

ACTIVITY - Inactivity should be avoided by all means, it only leads us to be
nonsensical. Activity implies resistance. Resist all evils, mental and physical and when you have learnt to do this without fear or favour you will find calmness around you and peace of mind to give you company.

AFFLICTION - Contrary to what might be expected, I look back on experience, that at the time seemed desolating and painful, with particular satisfaction. Indeed everything I have learnt, everything that has truly enhanced and enlightened my existence has been through 'affliction' and through 'happiness'. If it were to be possible to eliminate affliction from our earthly existence, the result would not be to make life delectable, but to make it too banal and trivial to be endurable.