### Rationals Between...

What fractions can you find between the square roots of 65 and 67?

### Root to Poly

Find the polynomial p(x) with integer coefficients such that one solution of the equation p(x)=0 is $1+\sqrt 2+\sqrt 3$.

### Consecutive Squares

The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?

# Powers of Four

##### Age 14 to 16 Short Challenge Level:

$4^x+4^x+4^x+4^x = 4 \times 4^x$ = $4^{x+1}$
So $x+1=16$, hence $x = 15$