## Solution to Puzzle #4: Summing to 15

This was probably a more difficult problem that what I had anticipated this to be. I got much fewer responses for this compared the previous ones. This puzzle combined two different concepts – Magic Square using numbers 1-9 and the tic-tac-toe game to arrive at the answer. Here is a link to the solution:

Hope you enjoyed this, and are looking forward to the next one, which is a relatively simpler one.

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### 5 Responses to Solution to Puzzle #4: Summing to 15

1. chaitanya.aggarwal@gmail.com says:

Hi Chacha, i came up with a number matrix (magic square) which is mirror image of yours and I was using the same concept of ‘kaanta-zero’ game, however I was stuck trying to come up with a winning strategy. All I came up was how not to lose. I thought the puzzle asked for a winning strategy. Enjoyed this puzzle.

2. Ravi Khanna says:

Another way to look at a solution or the best strategy without using the grid, is to see the sets 3 numbers between 1-9, you realize that 5 occurs the largest number of times in all such sets. Incidentally, the grid you drew also has 5 in the centre. The one picking up 5 remains most likely to win just as in ttt, the first mover marking the centre is the least likely to lose.

• Alok Goyal says:

Agreed Ravi, but the thing is that even selecting 5 first does not guarantee a win. Similar to a tic-tac-toe, where someone selects the center, but still cannot guarantee a win unless the opponent commits a mistake.

3. Alok Mittal says:

Alok mentioned that the audience for this blog seems to be mostly IITians and their kids. For the moms and dads, here is a dissertation – http://www.austms.org.au/Gazette/2005/Jul05/mathellaneous.pdf

Note that translation of the problem from picking numbers to tic-tac-toe is not a proof that a winning strategy does not exist. This file provides the proof, and suggest many interesting variations.

Enjoy!

4. When I talked to my son, Sahil, about this game he mentioned that this also appears in the delightful book “Aha, Insight” (http://www.amazon.com/Aha-Insight-Martin-Gardner/dp/071671017X) by Martin Gardner.

Gardner gives this interesting isomorphic game. Quoting from the book..

It is played with these nine words:

HOT
TANK
TIED
FORM
HEAR
BRIM
WOES
WASP
SHIP

Two players take turns crossing out a word and initialing it. The first player who crosses out three words that have the same letter in common is the winner.