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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?
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Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
Sweets in a Box
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
Age 7 to 11
Challenge Level
In the $2 \times 2$ multiplication square below, the boxes at the end of each row and the foot of each column give the result of multiplying the two numbers in that row or column.
| 7 | 5 | 35 |
| 3 | 4 | 12 |
| 21 | 20 |
The $3 \times3$ multiplication square below works in the same way. The boxes at the end of each row and the foot of each column give the result of multiplying the three numbers in that row or column.
| 15 | |||
| 108 | |||
| 224 | |||
| 144 | 8 | 315 |
The numbers $1 - 9$ may be used once and once only.
Can you work out the arrangement of the digits in the square so that the given products are correct?
NRICH is part of the family of activities in the Millennium Mathematics Project.