I have long been a subscriber of Lockergnome, especially Windows Fanatics. One column which I often look forward to reading is Sherman's Thinkers by Sherman E. Deforest. In this column, he discusses about decision theory, and often posts some interesting puzzles to ponder upon. I like how he usually relates his discussions with intriguing examples, making it much much easier to understand. For a person which a short attention span (me!) who can never make it through papers which seem to be written in a completely different language, this is indeed refreshing.

Anyway, I found one of his latest puzzles quite interesting. I'll just summarise the puzzle: 2 integers (from 1 to 9) are chosen, and 2 players (the Adder and the Multiplier) are only given the sum and product of these 2 integers respectively. "Adder" and "Multiplier" are only allowed to tell each other whether they know the answer. Now, they have to guess the 2 integers!

"Multiplier" thinks and says "I don't know".

"Adder" thinks and says "I don't know".

"Multiplier" thinks and says "I don't know".

"Adder" thinks and says "I don't know".

"Multiplier" thinks and says "I don't know".

"Adder" thinks and says "I don't know".

"Multiplier" thinks and says "I don't know".

"Adder" thinks and says "I don't know".

"Multipler" thinks and says "I know! I know!" and gives the correct answer! Yippee!

How and why? There are lots of hints in his article. I'm too lazy to type it out, but it has something to do with elimination.

I have managed to solve it, and I even whipped up a Python program to double check, and it matches! (^_~)

Hurrah!

### Guess the Integers!

22 March 07

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