Jack's Number Conundrum

Logic Level 1

One day, Jack decides to give his friends Alice and Bob an "impossible" challenge:

"I am thinking of an integer between 1 1 and 80. 80. I will tell Alice its prime factors (not raised to their exponents), and Bob the digit sum of the integer. Then, I would like you to figure out my number. However, you are forbidden to tell each other the information I've given you."

After handing out the promised information, Jack witnesses this exchange:

Alice: "I do not know the number."

Bob: "How many prime factors does your number have?"

Alice: "Three."

Bob: "Then I know the number."

Alice: "And so do I."

What is Jack's number?

Assume that Alice and Bob are perfect logicians, and made no computational errors.


The answer is 30.

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2 solutions

Possible numbers are: 30, 42, 60, 66, 70, 78.

At first Alice cannot figure it out which means that the number has it's multiple among the possible numbers.

Hence, the number will be either 30 or 60.

After knowing the number of prime factors, Bob figured out the number which means that only 1 number in the list have the sum which is told to him.

Hence, 60 is excluded.

From the given scenario, Bob figured out that the number is 30.

Since Bob could figure out the number, Alice understood the situation and figured out the number.

You Con
Aug 30, 2018

Got this one on second try. I know how Bob got answer, but I dont know how Alice figured it out. Based on info provided, I would think Alice would still be stuck between 30 & 60. What did I miss?

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