# Two Math Questions for all of you geniuses...

**54**Junior Member

In a certain game, each token has one of three possible values: 1 point, 5 points, or 10 points. How many combinations of these token values are worth a total of 17 points?

Correct answer: Six

How do you solve this other than just listing them out and hoping you don't miss one? Or is that it?

Blue Book Test 3 Part 8: #16

A cube with volume 8 cubic centimeters is inscribed in a sphere so that each vertex of the cube touches the sphere. What is the length of teh diameter, in centimeters, of the sphere?

Correct answer: 2(sqrt3) - about 3.46

I solved this by approximating, but I'd like to know how to truly solve it.

Thank you in advance.

## Replies to: Two Math Questions for all of you geniuses...

174Junior Member3,228Senior MemberStart by finding out how many combinations have a 10.

10 + 5 + two-ones

10 + seven-ones

Then how many combinations have one or more 5s (we've already dealt with 10s above ... so none of these have a ten)

5 + twelve-ones

two-5s + 7-ones

three-5s + 2-ones

Then how many combinations have only ones

seventeen-ones

Try a similar problem -- same rules -- except the sum is 26 and in addition to 10, 5 and 1 point pieces you also have 25 point pieces.