Mursalin's Magnificent Mustache and his Magical Razor

Number Theory Level 3

After many years of "No shave New Years resolutions," Mursalin finally decides to shave his magnificent mustache of 2014 hairs. Each hair is randomly assigned a number from 1 to 2014 such that no two have the same number.

However, he just so happens to have a magical razor with an infinite amount of blades. Each blade is assigned a number from 1 to ℵ 0 \aleph_0 such that each blade cuts every hair which is a multiple of that razor's number. The first blade is defective and only cuts the first hair then breaks.

What is the number on the blade that cuts the last hair?


The answer is 2011.

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Trevor Arashiro by Trevor Arashiro , 22, USA

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2 solutions

Jake Lai
Dec 17, 2014

The problem is equivalent to Erastothenes' sieve, and thus it looks for the greatest prime below 2014. A quick check shows that 2011 is the prime we need.

4 Helpful 0 Interesting 0 Brilliant 0 Confused
Vishal S
Dec 31, 2014

When the blade cuts 2nd hair,it's multiples will be cut off.When the blade cuts 3rd blade,its multiple will be cut off and so on, only prime numbers will be remained back.

By cutting of each prime number's hair, 2011 will be remained back as it is the last prime number from 1 to 2014.So the number on the last razor blade is 2011

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