November 2005
Shapes
A man wishes to leave his land to be shared equally between his four children. He wants to give each child a piece of land which is the same shape as well as the same size. Unfortunately, his land has a rather awkward shape, as you can see in the diagram.
Can you show how to divide this shape into four congruent pieces?
Numbers
In the equations below, the eight letters a to h represent different, single-digit numbers between 1 and 9.
| ab × ba = c(c - 1) |
| de × ed = a(a - 1) |
| f = g2 - a2 |
| hb = ga |
Which number between 1 and 9 is not used? (You will need to work out the number that each letter represents.)
Algebra
The diagram shows an isosceles triangle ABC with AB = AC. D is a point on AC and BCD is another isosceles triangle with BC = BD. Angle ABD = 24°.
Find angle BAC.
(Hint: This is an algebra puzzle.)
Miscellaneous
Tweedledum and Tweedledee look alike, but they lie on different days of the week. Tweedledum lies on Monday, Tuesday, and Wednesday, whereas Tweedledee lies on Thursday, Friday, and Saturday. They both tell the truth on Sunday. One day you meet Tweedledum and Tweedledee, but you cannot tell which is which. They make the following statements:
A: Today is not Sunday.
B: Today is not Monday.
Which of A and B is Tweedledum, and which is Tweedledee? What day of the week is it?