What fractions can you find between the square roots of 56 and 58?
Find the polynomial p(x) with integer coefficients such that one solution of the equation p(x)=0 is $1+\sqrt 2+\sqrt 3$.
The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?
There are three ways to enter the triangular array of numbers in the
diagram below, starting with 1, and counting from 1 -2 in order,
finishing with the two in the bottom row.
How many ways are there to count 1 - 2 - 3 in the following array?
And 1 - 2- 3 - 4 on this?
Can you generalize?
Can you explain what you find?