Two bins

Number Theory Level 2

The numbers 1 through n n (inclusive) are separated into 2 bins.

For each bin, no two different numbers in it can add up to a prime number.

What is the largest n n for which this is possible?

If you think the answer is infinite, please put 99999 as your answer.


The answer is 99999.

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Geoff Pilling by Geoff Pilling , 53, USA

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2 solutions

Geoff Pilling
Nov 14, 2016

No matter how high n n is, you can put the even numbers in one bin and the odd numbers in the other one. Since any two numbers will always add up to an even number greater than two, the answer is ∞ \boxed{\infty}

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Very nice split!

Calvin Lin Staff - 4 years, 7 months ago

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Thanks! :) ......

Geoff Pilling - 4 years, 7 months ago

Very nice!

Follow-up exercise: prove that, for any n n , the even/odd split is the only possible way to split the numbers.

Hint

Tijmen Veltman - 4 years, 7 months ago

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Ah yes... Likely a much more interesting question! :)

Geoff Pilling - 4 years, 7 months ago

they asked for 9999 so it was obvious

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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