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Follow the clues to find the mystery number.

Prime Magic

Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?

Diagonal Trace

You can trace over all of the diagonals of a pentagon without lifting your pencil and without going over any more than once. Can the same thing be done with a hexagon or with a heptagon?

Sets of Four Numbers

Age 7 to 11 Challenge Level:

Miss Brown was working with Becky's group on numbers that share a certain property. She wrote twelve numbers on the board.

numbers 2, 3, 4, 5, 7, 9, 10, 15, 21, 25, 28, 49

"You can all find a different set of just four numbers that go together," she said, "And they must have a proper mathematical name. They can't be just a set of numbers that you like!"

The children stared at the numbers. Alan put up his hand. "Like odd numbers?" he suggested.
"That's the right idea," said Miss Brown, "but you can't choose just odd numbers because there are more than four of them. You must use all the numbers in my list which fit your set. Anyone else got an idea?"
Becky put her hand up. "Numbers in the $5$ times table? There are four of those."
"That's right. But what would be a good name for them?"
"Multiples of $5$?" suggested Becky.
"Good," said Miss Brown and she wrote on the board:

numbers above with Becky's set written: 5, 10, 15, 20
There are ten children in Becky's group.
Can you find a set of numbers for each of them?
Are there any other sets?