Puzzles, Issue 02

Seven Digits

Source: My Best Puzzles in Mathematics by Hubert Phillips
I’m thinking of a number. I’ve squared it. I’ve squared the square. And I’ve multiplied the second square by the original number.

So I now have a number of seven digits whose final digit is a seven.

What was my original number?

Odd Squares

How many square numbers are there whose digits are all odd?

Folding Tube Maps

Source: mscroggs.co.uk
In How To Make, you will find the instructions for folding a tetrahedron from two tube maps.

The resulting tetrahedron is almost (but not quite) regular.

What ratio would the sides of the tube maps have to be to make a regular tetrahedron?