Alex, Max, Primes and whatnot

Logic Level 3

Alex and Max are given two different prime numbers, and the following dialogue ensues:

Alex: I don't know which of our numbers is greater.

Max: Then my number is not the greater one for sure.

What is the largest possible sum of their numbers, provided both the numbers are below 100 (but Alex and Max don't know that 100 is the upper bound)?


The answer is 100.

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Shashank Rammoorthy by Shashank Rammoorthy , 20, India

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2 solutions

At first, Alex does not know which of the two prime numbers are greater. This implies that his number is surely not 2, as then it would be obvious.

When Alex states the obvious, Max immediately replies by saying his number is not the greater one. Thus, we come to the conclusion that Max's number is 3. Before Alex's statement, Max was doubtful. But now that Alex indirectly stated that his number was not 2, Max is sure his number is lesser.

The largest possible sum of the two numbers is 3 + 97 = 100. This is because 97 is the largest prime lesser than a hundred.

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Moderator note:

Nice simple problem!

If one of them had the smallest prime number which is "2" he would simply knew that the other guy's number is greater one.

The only case that makes Max sure that he has the smallest among them both after hearing Alex sentence is when he has the 2nd smallest prime which is "3"

Now we know that 97 is greatest prime under 100

so the answer=3+97=100

2 Helpful 0 Interesting 0 Brilliant 0 Confused

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