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Algebra > Diophantine equations

##### Age 11 to 14 Challenge Level:

When asked how old she was, the teacher replied: My age in years is
not prime but odd and when reversed and added to my age you have a
perfect square...

##### Age 11 to 14 Challenge Level:

What are the possible dimensions of a rectangular hallway if the number of tiles around the perimeter is exactly half the total number of tiles?

##### Age 11 to 14 Challenge Level:

Can you work out how many of each kind of pencil this student
bought?

##### Age 11 to 14 Challenge Level:

The well known Fibonacci sequence is 1 ,1, 2, 3, 5, 8, 13, 21....
How many Fibonacci sequences can you find containing the number 196
as one of the terms?

##### Age 11 to 14 Challenge Level:

According to Plutarch, the Greeks found all the rectangles with
integer sides, whose areas are equal to their perimeters. Can you
find them? What rectangular boxes, with integer sides, have. . . .

##### Age 11 to 14 Challenge Level:

If: A + C = A; F x D = F; B - G = G; A + H = E; B / H = G; E - G =
F and A-H represent the numbers from 0 to 7 Find the values of A,
B, C, D, E, F and H.