Mona Lisa on world Tour



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Monalisa After One Week in Africa





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After visiting India

1. Marriage is not a word. It's a sentence (a life sentence).

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2. Marriage is love. Love is blind. Therefore marriage is an institution for the blind.



3. Marriage is an institution in which a man loses his Bachelor's Degree and the woman gets her masters.



4. Marriage is a three-ring circus: engagement ring, wedding ring and suffeRING.



5. Married life is full of excitement and frustration: In the first year of marriage, the man speaks and the woman listens. In the second year, the woman speaks and the man listens.In the third year, they both speak and the NEIGHBOUR listens.



6. Getting married is very much like going to a restaurant with friends.You order what you want, and when you see what the other person has, you wish you had ordered that instead.



7. There was this man who muttered a few words in the church and found himself married. A year later he muttered something in his sleep and found himself divorced.



8. A happy marriage is a matter of giving and taking; the husband gives and the wife takes.



9. Son: How much does it cost to get married, Dad? Father: I don't know son, I'm still paying for it.



10. Son: Is it true Dad? I heard that in ancient China, a man doesn't know his wife until he marries her. Father: That happens everywhere, son, EVERYWHERE!



11. Love is one long sweet dream, and marriage is the alarm clock.



12. They say that when a man holds a woman's hand before marriage, it is love; after marriage it is self-defense.



13. When a newly married man looks happy, we know why. But when a 10-year married man looks happy, we wonder why.



14. There was this lover who said that he would go through hell for her. They got married, and now he is going through HELL.



16. When a man steals your wife, there is no better revenge than to let him keep her.



17. Eighty percent of married men cheat in America, the rest cheat in Europe.



18. After marriage, husband and wife become two sides of a coin. They just can't face each other, but they still stay together.



19. Marriage is man and a woman become one. The trouble starts when they try to decide which one.



20. Before marriage, a man yearns for the woman he loves. After the marriage the "Y" becomes silent.



21. I married Miss right; I just didn't know her first name was Always.



22. It's not true that married men live longer than single men, it only seems longer.



23. Losing a wife can be hard. In my case, it was almost impossible.



24. A man was complaining to a friend: I HAD IT ALL-MONEY, A BEAUTIFUL HOUSE, THE LOVE OF A BEAUTIFUL WOMAN, THEN POW! IT WAS ALL GONE. WHAT HAPPENED, asked his friend. He says MY WIFE FOUND OUT.



25. WIFE: Let's go out and have some fun tonight. HUSBAND: OK, but if you get home before I do, leave the hallway lighs on.



26. At a cocktail party, one woman said to another: AREN'T YOU WEARING YOUR RING ON THE WRONG FINGER? The other replied, YES, I, AM. I MARRIED THE WRONG MAN.



27. Man is incomplete until he gets married, then he is finished.



28. It doesn't matter how often a married man changes his job, he still ends up with the same boss.



29. A man inserted an ad in the paper - WIFE WANTED. The next day he received a hundred of letters and they all said the same thing - YOU CAN HAVE MINE.



30. When a man opens the door of his car for his wife, you can be sure of one thing - either the car is new or the wife is.

 

A number is divisible by 2 if its last digit is also (i.e. 0,2,4,6 or 8).

A number is divisible by 3 if the sum of its digits is also. Example: 534: 5+3+4=12 and 1+2=3 so 534 is divisible by 3.

A number is divisible by 5 if the last digit is 5 or 0.

Most people know (only) those 3 rules. Here are my rules for divisibility by the PRIMES up to 50. Why only primes and not also composite numbers? A number is divisible by a composite if it is also divisible by all the prime factors (e.g. is divisible by 21 if divisible by 3 AND by 7). Small numbers are used in these worked examples, so you could have used a pocket calculator. But my rules apply to any number of digits, whereas you cannot test a 30 or more digit number on your pocket calculator otherwise.

Test for divisibility by 7. Double the last digit and subtract it from the remaining leading truncated number. If the result is divisible by 7, then so was the original number. Apply this rule over and over again as necessary. Example: 826. Twice 6 is 12. So take 12 from the truncated 82. Now 82-12=70. This is divisible by 7, so 826 is divisible by 7 also.

There are similar rules for the remaining primes under 40, i.e. 11,13, 17,19,23,29,31,37,41,43 and 47.

Test for divisibility by 11. Subtract the last digit from the remaining leading truncated number. If the result is divisible by 11, then so was the first number. Apply this rule over and over again as necessary.

Example: 19151--> 1915-1 =1914 -->191-4=187 -->18-7=11, so yes, 19151 is divisible by 11.

Test for divisibility by 13. Add four times the last digit to the remaining leading truncated number. If the result is divisible by 13, then so was the first number. Apply this rule over and over again as necessary.

Example: 50661-->5066+4=5070-->507+0=507-->50+28=78 and 78 is 6*13, so 50661 is divisible by 13.

Test for divisibility by 17. Subtract five times the last digit from the remaining leading truncated number. If the result is divisible by 17, then so was the first number. Apply this rule over and over again as necessary.

Example: 3978-->397-5*8=357-->35-5*7=0. So 3978 is divisible by 17.

Test for divisibility by 19. Add two times the last digit to the remaining leading truncated number. If the result is divisible by 19, then so was the first number. Apply this rule over and over again as necessary.

EG: 101156-->10115+2*6=10127-->1012+2*7=1026-->102+2*6=114 and 114=6*19, so 101156 is divisible by 19.

Test for divisibility by 23. Add seven times the last digit to the remaining leading truncated number. If the result is divisible by 23, then so was the first number. Apply this rule over and over again as necessary.

Example: 17043-->1704+7*3=1725-->172+7*5=207-->20+7*7=69 which is 3*23, so 17043 is also divisible by 23.

Test for divisibility by 29. Add three times the last digit to the remaining leading truncated number. If the result is divisible by 29, then so was the first number. Apply this rule over and over again as necessary.

Example: 15689-->1568+3*9=1595-->159+3*5=174-->17+3*4=29, so 15689 is also divisible by 29.

Test for divisibility by 31. Subtract three times the last digit from the remaining leading truncated number. If the result is divisible by 31, then so was the first number. Apply this rule over and over again as necessary.

Example: 7998-->799-3*8=775-->77-3*5=62 which is twice 31, so 7998 is also divisible by 31.

Test for divisibility by 37. This is (slightly) more difficult, since it perforce uses a double-digit multiplier, namely eleven. People can usually do single digit multiples of 11, so we can use the same technique still. Subtract eleven times the last digit from the remaining leading truncated number. If the result is divisible by 37, then so was the first number. Apply this rule over and over again as necessary.

Example: 23384-->2338-11*4=2294-->229-11*4=185 which is five times 37, so 23384 is also divisible by 37.

Test for divisibility by 41. Subtract four times the last digit from the remaining leading truncated number. If the result is divisible by 41, then so was the first number. Apply this rule over and over again as necessary.

Example: 30873-->3087-4*3=3075-->307-4*5=287-->28-4*7=0, remainder is zero and so 30873 is also divisible by 41.

Test for divisibility by 43. Now it starts to get really difficult for most people, because the multiplier to be used is 13, and most people cannot recognise even single digit multiples of 13 at sight. You may want to make a little list of 13*N first. Nevertheless, for the sake of completeness, we will use the same method. Add thirteen times the last digit to the remaining leading truncated number. If the result is divisible by 43, then so was the first number. Apply this rule over and over again as necessary.

Example: 3182-->318+13*2=344-->34+13*4=86 which is recognisably twice 43, and so 3182 is also divisible by 43.

Finally, the Test for divisibility by 47. This too is difficult for most people, because the multiplier to be used is 14, and most people cannot recognise even single digit multiples of 14 at sight. You may want to make a little list of 14*N first. Nevertheless, for the sake of completeness, we will use the same method. Subtract fourteen times the last digit from the remaining leading truncated number. If the result is divisible by 47, then so was the first number. Apply this rule over and over again as necessary.

Example: 34827-->3482-14*7=3384-->338-14*4=282-->28-14*2=0 , remainder is zero and so 34827 is divisible by 47.

I have displayed the recursive divisibility test of number N as f-M*r where f are the front digits of N, r is the rear digit of N and M is some multiplier. And we want to see if N is divisible by some prime P. We need a method to work out the values of M. What you do is to calculate (mentally) the smallest multiple of P which ends in a 9 or a 1. If it's a 9 we are going to ADD, if it's a 1 we are going to SUBTRACT later. Then we will use the leading digit(s) of the multiple as our multiplier M.

Example for P=17 : three times 17 is 51 which is the smallest multiple of 17 that ends in a 1 or 9. Since it's a 1 we are going to SUBTRACT later. The leading digit is a 5, so we are going to SUBTRACT five times the remainder r. The algorithm was stated above. Now let's do the algebraic proof. Writing N=10f+r, we can multiply by -5 (as shown in the example for 17), getting -5N=-50f-5r. Now we add 51f to both sides (because 51 was the smallest multiple of P=17 to end in a 1 or a 9), giving one f (which we want), so 51f-5N=f-5r. Now if N is divisible by P (here P=17), we can substitute to get 51f-5*17*x=f-5r and rearrange the left side as 17*(3f-5x)=f-5r and therefore f-5r is a multiple of P=17 also. Q.E.D.