Question 24

The largest three digit number with the property that the number is equal to the sum of the hundreds digit, the square of its tens digit and the cube of its units digit is $$\underline{\qquad}$$.

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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The largest three digit number with the property that the number is equal to the sum of the hundreds digit, the square of its tens digit and the cube of its units digit is $$\underline{\qquad}$$.

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