Probability With an Unordinary Dice

Number Theory Level pending

You are rolling a dice with 200 sides, numbered 1 - 200. What is the probability that the side you rolled will contain a number that can be expressed as the sum of of two cubes in two different ways?

There is no such possibility. 1/100 5/200 The possibility of this happening is less than 1 1/40 1/200

Vishruth Bharath by Vishruth Bharath , 17, USA

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1 solution

Vishruth Bharath
Dec 26, 2017

As the great mathematician Srinivasa Ramanujan once stated, "1729 is the smallest number expressible as the sum of two cubes in two different ways." Here, we are told that there are only 200 sides that are numbered 1 through 200. Since it does not contain the number 1729, there is no such possibility of rolling a number that can be expressed as the sum of two cubes in two different ways.

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1729 1729 is the smallest integer expressible as the sum of two cubes of positive integers in two different ways. There is also 91 = 3 3 + 4 3 = 6 3 − 5 3 91=3^3+4^3=6^3-5^3 and - by some definitions - 1 = 1 3 + 0 3 = 1 3 − 0 3 1=1^3+0^3=1^3-0^3 . So there is at least one solution and depending on definition possibly two.

Chris Lewis - 1 year, 7 months ago

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