Peculiar number

Number Theory Level 2

If X X is a positive number and when on squaring and cubing , it is found that the obtained numbers have distinct digits in both cases below. X 2 = a 0 a 1 a 2 a 3 ‾ X 3 = a 4 a 5 a 6 a 7 a 8 a 9 ‾ X^2 = \overline{a_0a_1a_2a_3} \qquad X^3 = \overline{a_4a_5a_6a_7a_8a_9} What is the number X ? X\,?

Note: Both of the cases in total has 10 distinct digits from 0 to 9 .


The answer is 69.

Naren Bhandari by Naren Bhandari , 21, India

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1 solution

Giorgos K.
Apr 15, 2018

I used M a t h e m a t i c a Mathematica to solve this:

Select[Range@100,Sort@Join[IntegerDigits[#^2],IntegerDigits[#^3]]==Range[0,9]&]

which gave the right answer 69 69

0 Helpful 0 Interesting 0 Brilliant 0 Confused

The number can't end in 5, 6 or 1 as these numbers end in the same digit when squared and cubed. I used python to solve it and can't think of any better way than trial and error

Theodore Sinclair - 3 years, 1 month ago

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