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Cut it Out

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

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Zios and Zepts

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

The Deca Tree

Age 7 to 11 Challenge Level:

In the forest there is a Deca Tree.
A Deca Tree has $10$ trunks,

tree with 10 trunks

and on each trunk there are $10$ branches,

trunk with 10 branches

and on each branch there are $10$ twigs,

branch with 10 twigs

and on each twig there are $10$ leaves:

twig with 10 leaves

One day a woodcutter came along and cut down one trunk from the tree.
Then he cut off one branch from another trunk of the tree.
Then he cut off one twig from another branch.
Finally he pulled one leaf from another twig.

How many leaves were left on the tree then?

Click here for a poster of this problem.