Question 24
The largest three-digit number that equals the sum of its hundreds digit, the square of its tens digit and the cube of its units digit is
Correct Answer: 598
Solution
Let the number be $$100h+10t+u$$. The condition becomes $$99h+10t=t^2+u^3$$ for digits $$h,t,u$$. Checking the digit possibilities gives the solutions $$135,175,518,598$$, of which the largest is $$598$$.
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