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# Frosty the Snowman

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Age 16 to 18

Challenge Level

- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

Walter from Abingdon School in the UK sent in this full solution to the first part of the problem (click here to see a larger version):

Walter's solution to the second part of the problem is almost perfect (click here to see a larger version):

Once Walter realises that the top snowball is completely melted (and has a negative radius), Walter removes that snowball from the volume calculation - which is correct.

However, Walter should have recalculated the radius of the remaining snowball using the new information that the smaller snowball had disappeared.

What should the answer be?

This problem asks you to use your curve sketching knowledge to find all the solutions to an equation.

Can you find a three digit number which is equal to the sum of the hundreds digit, the square of the tens digit and the cube of the units digit?

How many numbers are there less than $n$ which have no common factors with $n$?