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## 'Code to Zero' printed from http://nrich.maths.org/

Find all the 3 digit numbers such that by adding the first
digit, the square of the second digit and the cube of the third
digit you get the original number, for example $1 + 3^2
+ 5^3 = 135$. Can you find ways of reducing the search
so that you do not need to test 900 cases?

[This problem appears in Ken Follett's spy thriller of the same
name].