One of you two, out there, ate the last piece of cake we were hoping to save for grandma. I can figure out who did it without even checking your sticky fingers and dirty teeth. Whoever did it, pick any odd number. Whoever didn't do it, pick any even number. But be honest! Now, you, standing closer to me, multiply your number by 2. The other person - multiply your number by 3. Share your numbers with each other and tell me their sum. As soon as I hear this sum, I can now figure out who ate the cake! How?

(this puzzle is inspired by a story from B. Kordemsky book)

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## 5 comments:

Interesting puzzle!

I'm just going to choose two numbers to see what happens - let's say 7 and 8.

7 X 2 = 14 and 8 x 3 = 24. Adding these two get 38.

What if it was the other way around?

7 x 3 = 21 and 8 x 2 = 16. Adding these two get 37.

In other words, you're getting information based on multiplication - if you multiply the odd number by 3, you will still get an odd number and multiplying the odd number by 2 will get you an even number. With the even number, it does not matter what you multiply with it, it will be even.

So by hearing the sum, you know that if it is odd, whoever multiplied by 3 (the other person aka the person standing farther away from you) picked the odd number and ate the last piece of cake. Otherwise, it is the person closer to you.

If the sum is odd, then it was the odd number that was multiplied by 3, and the "3 multiplier" person is standing farther from you.

If the sum is even, the odd number was multiplied by 2, that is, by the person closest to you.

Odd is guilty.

Even sum: guilty is closer to you

Odd sum: guilty is farther from you

Assuming the little bandits are telling the truth!

Tom

You both are right and it even seems like Tom didn't see Wang's answer when he replied. Still puzzle point goes to the first one only. 16th point for Wang!

I'm okay with being beaten. Tell us again what time the puzzles "go up" though? Tom

Puzzles are posted usually around 10am Eastern Time on Friday. Unless I am traveling and then it is unpredictable.... In any case, newsletter containing the puzzles is sent just a few minutes after puzzles are posted.

I know that it is not really a fair game for everyone. It is tough to do puzzles at 7am Pacific time before finishing your first cup of coffee. And much easier when you comfortably solved all the morning fires at work and looking for something fun to do before lunch.

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