Building Tetrahedra

Can you make a tetrahedron whose faces all have the same perimeter?

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

Ratio Riddle

Stage: 4 Short Challenge Level:

The ratio $a : b = 2 :3$ and the ratio $a : c = 3 : 4$. What is the ratio $b : c$?                                                                                                                                                                                                                         If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
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