How many right-angled triangles are there with sides that are all
integers less than 100 units?
A square patio was tiled with square tiles all the same size. Some
of the tiles were removed from the middle of the patio in order to
make a square flower bed, but the number of the remaining tiles was
still a square number. What were the dimensions of the patio and
the flower bed?
A woman was born in a year that was a square number, lived a square
number of years and died in a year that was also a square number.
When was she born?
If the number of tiles used originally was x
2 and the total number of tiles used was y
2 , then :
x 2 + 100 = y 2
x 2 + 10 2 = y
This is a Pythagorean triple (see Pythagorean Triples ) which can be
satisfied by x = 24 with y = 26.
So total number of tiles = 26 2 = 676
Correct solution from Adrian from South
Greenhoe Middle School.