Mathematics can be quite interesting.

[CLN]

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Fair enough! If zebra16 or any one else does not post the steps, I will post myself, madam. Let us give time till, say, 7 a.m. IST of 23 June, 2011.

 

[zebra16]

If you DO NOT mind, can you please tell us how you arrived at the solution?

Namaste,

The only possible number in 5th column (at the 10,000th place) is 1, so M = 1. To ensure a carry over to the next column, and because M=1, S has to be equal to 9. If there is no carry over from third column to fourth column E should be equal to 9 (because O = 0). E cannot be 9, as S is already 9. So there is carry over. If there is no carry over from second column to third column, then E = N, which is ruled out by the problem setter. So N = E + 1. I could have continued logically to second column and first column, but since I had already three sure values for S, E, and O, and derivative value for N, and D and Y being relatively unimportant, I tried to guess the value of E, which is repeating thrice in the equation. In the second try I guessed it as 5, so N became 6. D and Y had to be any unused digits, but which gave a carry over. So they could be any two out of four digits of 2, 3, 4 and 7 and it is quite simple that 7 fits at the place of D because you need a carry over and no other figure adds up for a carry over. Y becomes 2 by simple addition of D + E. I hope you make sense out of my explanation.

I think modular arithmetic would have solved the problem in much quicker time.

Regards,

narayan

 

[biswa]

A tribute to our own Great Mathematician.

Srinivasa Ramanujan - Wikipedia, the free encyclopedia

I was totally expecting this reference! Are most Tamil Brahmins born with a mathematical spoon in their mouth? Is there anybody here who cannot solve a quadratic equation in their head? What do you think about Shakuntala Devi? Underappreciated genius?

 

[CLN]

Fair enough! If zebra16 or any one else does not post the steps, I will post myself, madam. Let us give time till, say, 7 a.m. IST of 23 June, 2011.

Madam VR, I am sure now you can feel relieved that zebra16 has risen to the occasion and posted the solution, as I expected. Maybe now, if you are still interested, you may try for the other solutions too, as I pointed out in my post #49! Happy puzzling!

Good work, Shri narayan!

 

[sravna]

I am still under the spell of the number 2519!. Here are some more observations. In 2520 you add 25 and 20 i.e. the first two and last two digits you get 45 which is the sum of the numbers from 1 to 9 by which 2520 is divible. Also 2520 can be written as 45 + 45 square + 450. Again there is this coincidence of 45. Seems interesting.

 

[sravna]

It seems to be there is a relation between the sum of the digits in a number taken in a certain way and the sum of the numbers divisible by it. It seems to be a little deep for me to get into now. Any mathematician among members may throw some light on this.

 

[zebra16]

There is an interesting tidbit about this "SEND + MORE = MONEY" puzzle. When I said SEND and MORE are 4-digit numbers and MONEY is a 5-digit number, it is automatically (and rightly too!) taken by any one that the left-most digits in these three numbers cannot be zero. But if this vital condition is not applied, the uniqueness of the solution is lost and there are several solutions to the puzzle! Any takers?

One possible answer: 3821 + 0468 = 04289

N.B.: I adopted a purely trial & error method, so I have nothing to offer by way of methodology. Would appreciate to know the methodology, though. I suppose there could be various answers, if the relationship between the letters (representing the integers) are maintained.

Regards,

narayan

 

[mskmoorthy]

French Open Tennis (Retrograde Analysis)

Now a question (may be trivial to all of you guys) of the recently concluded French Open Men's Tennis Finals. Assume most of you are experts in knowing the rules of Tennis.

1)Nadal won in the fourth set (and the match) with his serve.
2) Scores were 7-5,7-6,5-7,6-1
3) Second Set is a tie-breaker set.

Who served first in the first set? (Who started the match with a serve)
(some explanations will be helpful - instead of I watched from the beginning of the match )
I watched the tail end of this match and that is why I composed this puzzle!

This type of question is known as retrograde analysis - In Chess it is a bit more interesting. Interested readers may want to look at this link
Retrograde analysis - Wikipedia, the free encyclopedia

 

[srinikarthik]

Roger Fedrer Served first

 

[H.Krishnamurthy]

Dear Mr. Sravana,
Well as you made it clear the speciality of no 45.
It is not just 45 it is the no 9 which plays an important role in all these tricks.
You just read Table 9.
Sum of the 2 digits of the table is always going to be 9, till the term 2 nd 9 appears in the table. Again you add the result twice it is going to be 9 like 9X9 = 99: 9+9 = 18 again 1+ 8 = 9 again.
Like 0 being very important in all caluclation , 9 is equally so as it is going to decide the next digit, like from units it is going to Tens and so on so forth.
This is explained in Vedic Mathematics or Abaccus what they call now. ( Anyway I didnot get an oppurtunity to read this book ). My father used to solve my Pre university papers using this method. He used to solve Analytical geometry and other topics like Caluclus using Vedic Maths.
He was literated only upto 8 th Standard and was did his Vedic studies.
K.M.

 

[sravna]

Dear Mr. Sravana,
Well as you made it clear the speciality of no 45.
It is not just 45 it is the no 9 which plays an important role in all these tricks.
You just read Table 9.
Sum of the 2 digits of the table is always going to be 9, till the term 2 nd 9 appears in the table. Again you add the result twice it is going to be 9 like 9X9 = 99: 9+9 = 18 again 1+ 8 = 9 again.
Like 0 being very important in all caluclation , 9 is equally so as it is going to decide the next digit, like from units it is going to Tens and so on so forth.
This is explained in Vedic Mathematics or Abaccus what they call now. ( Anyway I didnot get an oppurtunity to read this book ). My father used to solve my Pre university papers using this method. He used to solve Analytical geometry and other topics like Caluclus using Vedic Maths.
He was literated only upto 8 th Standard and was did his Vedic studies.
K.M.

I agree Shri Krishnamurthy.. What seems to be a very convoluted connection might actually have a simple explanation.

 

[B.Krishnamurthy]

Number 9 seems to be significant.I happened to go through a book"Format Numerology"
by Dr.Mahha DAN Shekar Raajah.According to his theory there are 81 different group pf persons for each number from 1 to 9 and thus all who have already born and to be born
in future could be categorised under 729 groups.His Emai Id:[email protected].
The date of Birth of each person is the criteria for grouping a person under one of these 729 groups..I met him at his office cum residence in Neela kanta Mehta Street,Near Hindi Prachar Sabha,T'Nagar.Chennai.

 

[C RAVI]

Number 9 seems to be significant.I happened to go through a book"Format Numerology"
by Dr.Mahha DAN Shekar Raajah.According to his theory there are 81 different group pf persons for each number from 1 to 9 and thus all who have already born and to be born
in future could be categorised under 729 groups.His Emai Id:[email protected].
The date of Birth of each person is the criteria for grouping a person under one of these 729 groups..I met him at his office cum residence in Neela kanta Mehta Street,Near Hindi Prachar Sabha,T'Nagar.Chennai.

Sri B.Krishnamurthy,

I know him too. Have seen many of his TV programs and have found them all very interesting... Not only interesting, I could some how grasp his basic "Format Numerology" concept..

For example - Some one born on 21-JANUARY-1976, the person's numeric values as per Format Neumerology would be -

3-9-3 [3 is the date(2+1); 9 is the sume of dd/mm/yyyy and the third digit-3 is the sum of 3 & 9 )

It shows, the person has the dominent influence of Jupiter-Mars-Jupiter ...And based on these planetary presense and its positions in this number sequence, the impacts on the native can be revealed.

Since I am learning astrology/neumorology, I could make good sense of the above, could relate and see its relevance with the horoscop's planetary configuration, of the native.

 

[CLN]

To get back to the magic of numbers, from the mystique of numerology, here are some simple puzzles:

Find (a) THREE single digit numbers the sum of squares of which equals the square of another single digit number.

(b) THREE single digit numbers the sum of squares of which equals the square of two other single digit numbers. (two solutions available!)

(c) FOUR single digit numbers the sum of squares of which equals the square of another single digit number.

(d) FOUR single digit numbers the sum of squares of which equals the square of three other single digit numbers as well as two other single digit numbers.

Happy puzzling!

(Caution: 0 not allowed as one of the numbers!)

 

[zebra16]

To get back to the magic of numbers, from the mystique of numerology, here are some simple puzzles:

Find (a) THREE single digit numbers the sum of squares of which equals the square of another single digit number.

(b) THREE single digit numbers the sum of squares of which equals the square of two other single digit numbers. (two solutions available!)

(c) FOUR single digit numbers the sum of squares of which equals the square of another single digit number.

(d) FOUR single digit numbers the sum of squares of which equals the square of three other single digit numbers as well as two other single digit numbers.

Happy puzzling!

(Caution: 0 not allowed as one of the numbers!)

(a) (1 x 1) + (4 x 4) + (8 x 8) = (9 x 9)
(b) (1 x 1) + (2 x 2) + (6 x 6) = (4 x 4) + (5 x 5)
(c) (2 x 2) + (4 x 4) + (5 x 5) + (6 x 6) = (9 x 9)
(d) (3 x 3) + (4 x 4) + (6 x 6) + (7 x 7) = (2 x 2) + (5 x 5) + (9 x 9)

Regards,

narayan

 

[CLN]

Well done Shri narayan!

When I posted the puzzles I really was "apprehensive" )) that zebra16 would crack it fast; perhaps, I should have added a rider (!) that even if he solved, he may simply announce that he had solved it but should not post the solutions till after some time (say, a day or so!) (), so that others also would get a chance to try and post their solutions!

Ah, there is still hope! I intentionally excluded the Pythagorean triplet-related solutions (though I should have, perhaps, mentioned it - my mistake!) for all those puzzles, because they are so well-known.

So, though zebra16 has given some solution, for puzzle (d) (and he did not solve the puzzle fully), there is yet another solution! Any one interested ? (apart from zebra16, of course?)

For puzzle (b) also, there are still two more different solutions? Who is game for it?