I put eggs into a basket in groups of 7 and noticed that I could
easily have divided them into piles of 2, 3, 4, 5 or 6 and always
have one left over. How many eggs were in the basket?
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
Can you find a relationship between the number of dots on the
circle and the number of steps that will ensure that all points are
A and B are two interlocking cogwheels having p teeth and q
teeth respectively where $$3\leq q\leq p \leq
One tooth on B is painted red. Find the values of p and q for
which this red tooth on B contacts every gap on the cogwheel A as
the wheels rotate.