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Do you know the rhyme about ten green bottles hanging on a wall? If the first bottle fell at ten past five and the others fell down at 5 minute intervals, what time would the last bottle fall down?

How many were going to St Ives?

56 406 is the product of two consecutive numbers. What are these two numbers?

ABC and DEF are equilateral triangles of side 3 and 4 respectively. Construct an equilateral triangle whose area is the sum of the area of ABC and DEF.

Show that there are infinitely many rational points on the unit circle and no rational points on the circle x^2+y^2=3.

Find all 3 digit numbers such that by adding the first digit, the square of the second and the cube of the third you get the original number, for example 1 + 3^2 + 5^3 = 135.

Which has the greatest area, a circle or a square, inscribed in an isosceles right angle triangle?

In the limit you get the sum of an infinite geometric series. What about an infinite product (1+x)(1+x^2)(1+x^4)... ?