Special 24

Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.

Age

7 to 11

Challenge level

Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving

Being curious Being resourceful Being resilient Being collaborative

Problem

The number $24$ is special because it is just one short of being a square number.

So $24 + 1 = 25$ and $5^2 = 25$

AND when you double $24$ the answer is also one short of being a square

number.

So $24 \times 2 = 48$ and $48 + 1 = 49$ and $7^2 = 49$.

Find another number that is special in the same way as $24$.