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Rationals Between...

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

There's a Limit

Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you notice when successive terms are taken? What happens to the terms if the fraction goes on indefinitely?

Not Continued Fractions

Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?

Harmonic Triangle

Age 14 to 16
Challenge Level

Congratulations to Alice who sent in a correct solution to this problem:


solution

Congratulations to Ray who also worked on this problem and sent us the following result:

Ray's solution