You may also like

Modular Fractions

We only need 7 numbers for modulus (or clock) arithmetic mod 7 including working with fractions. Explore how to divide numbers and write fractions in modulus arithemtic.

Power Quady

Find all real solutions of the equation (x^2-7x+11)^(x^2-11x+30) = 1.

Areas and Ratios

Do you have enough information to work out the area of the shaded quadrilateral?

Water Pistols

Age 16 to 18 Challenge Level:

A group of children are in a field and no two pairs of children are at the same distance apart. Each child has a water pistol and shoots the child nearest to them.

For different numbers of children, can you construct configurations in which $0, 1, 2, 3, \cdots$ children get wet? Can you construct configurations in which $0, 1, 2, 3, \cdots$ children stay dry? Is there a largest or smallest number who could get wet in each case? Do any patterns emerge?

It is a hot day and all of the children want to get wet? Can you place them so that this is possible. Prove your results carefully.