Problems
Times
Stage:2 Challenge Level:
Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out!
Pebbles
Stage:2 and 3 Challenge Level:
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
Not a Polite Question
Stage:3 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...
The Lady or the Lions
Stage:3 Challenge Level:
The King showed the Princess a map of the maze and the Princess was allowed to decide which room she would wait in. She was not allowed to send a copy to her lover who would have to guess which path. . . .
On Time
Stage:3 Challenge Level:
On a clock the three hands - the second, minute and hour hands - are on the same axis. How often in a 24 hour day will the second hand be parallel to either of the two other hands?
Square Routes
Stage:3 Challenge Level:
How many four digit square numbers are composed of even numerals? What four digit square numbers can be reversed and become the square of another number?
Bi-cyclics
Stage:4 Challenge Level:
Two circles intersect at A and B. Points C and D move round one circle. CA and DB cut the other circle at E and F. What do you notice about the line segments CD and EF?
Same Height
Stage:4 Challenge Level:
A trapezium is divided into four triangles by its diagonals. Suppose the two triangles containing the parallel sides have areas a and b, what is the area of the trapezium?
Max Box
Stage:4 Challenge Level:
Three rods of different lengths form three sides of an enclosure with right angles between them. What arrangement maximises the area
Obviously?
Stage:4 and 5 Challenge Level:
Find the values of n for which 1^n + 8^n - 3^n - 6^n is divisible by 6.
Voting Paradox
Stage:4 and 5 Challenge Level:
Some relationships are transitive, such as `if A>B and B>C then it follows that A>C', but some are not. In a voting system, if A beats B and B beats C should we expect A to beat C?
