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:

Given that $4^x+4^x+4^x+4^x = 4^{16}$, what is the value of $x$?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.