Power of powers

Number Theory Level 3

A four digit number can be represented by ABCD. There is one number such that Can you find the smallest number? Note

  1. The numbers should not be 0 or 1
  2. B is not equal to C


The answer is 2592.

Shravan Kumar by Shravan Kumar , 28, India

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1 solution

Shravan Kumar
Sep 6, 2015

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How did you find this number? Is this the only 4 digit number that satisfy the condition?

Pi Han Goh - 5 years, 9 months ago

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It's the smallest number

Shravan Kumar - 5 years, 9 months ago

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How do you know that?

Pi Han Goh - 5 years, 9 months ago

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@Pi Han Goh – It's an example of Friedman number. A Friedman number is a positive integer which can be written in some non-trivial way using its own digits, together with the symbols + – × / ^ ( ) and *.

Since the digits in the expression are arranged in the same order as in the number itself, it comes under nice or orderly Friedman number.

The 4 digit nice Friedman numbers are 1285, 2187, 2502, 2592, 2737, 3125, 3685, 3864, 3972, 4096, 6455 and the only number satisfying the above condition is 2592.

Shravan Kumar - 5 years, 9 months ago

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@Shravan Kumar – Can you determine the solution without knowing that it's a Friedman number?

Pi Han Goh - 5 years, 9 months ago

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