All on a summer's day
The Queen of Hearts made 24 jam tarts. She arranged them in a square box so that the pattern was symmetrical and there were 9 tarts along each side of the box. The Jack of Hearts stole some of the tarts. He arranged the rest so that there were still 9 tarts in a symmetrical pattern along each side of the box.
How many tarts did the Jack of Hearts steal?
What was the new pattern?
DIGGING A HOLE
Hank the workman was 1.5 metres tall. He was standing upright in a hole he was digging.
"How much deeper are you going to dig?" asked Hank's mate.
"When I have finished the hole will be twice as deep," replied Hank. "My head will then be three times as far below the ground as it is now above it."
How deep was the final hole?
SOLUTIONS Digging a hole (ages 10 to 14). The final hole was 2.4 metres deep. It helps to represent the information in the problem in a diagram.
The thick lines show Hank. From this we can see that: h=(4.5 - 3h) + (1.5 - h), which gives h=1.2
All on a summer's day (ages 5 to 9) The Jack of Hearts stole 4 tarts and arranged the rest like this: