### Shades of Fermat's Last Theorem

The familiar Pythagorean 3-4-5 triple gives one solution to (x-1)^n + x^n = (x+1)^n so what about other solutions for x an integer and n= 2, 3, 4 or 5?

### Exhaustion

Find the positive integer solutions of the equation (1+1/a)(1+1/b)(1+1/c) = 2

### Code to Zero

Find all 3 digit numbers such that by adding the first digit, the square of the second and the cube of the third you get the original number, for example 1 + 3^2 + 5^3 = 135.

# In Between

##### Age 16 to 18 Challenge Level:

Find the range of values of $x$ for which
$${\sqrt{x}+ {{1}\over{\sqrt{x}}}} < {4}\,,$$
where $\sqrt{x}$ is the positive root.