Can you solve it? Puzzles for blockheads

IAN DURY AND THE BLOCKHEADS on a Dutch TV show in 1979 Photograph: Pictorial Press Ltd/Alamy

Today’s questions come from this year’s Mathigon puzzle advent calendar. One of the many reason to be cheerful (Pt. 3) at this time of year.

If you have a head for blocks, the first one is for you.

1. Hit me with your four cube stick

Every cube needs to touch at least one other cube. Faces have to line up. Ignore rotations and reflections. Don’t rush this one! It is very easy to miss obvious constructions. Photograph: Mathigon

2. Timelines

Don’t include the times when the hands coincide. Photograph: Mathigon

3. Eight heavy adult females

If that was too easy, can you make 100? Or 10? Photograph: Mathigon

4. Slice of orange

A familiarity with the Pythagorean theorem may help. It says that for right-angled triangles, the square of the hypotenuse is equal to the squares of the other two sides Photograph: Mathigon

.5. Bucket list

All today’s puzzles were taken from the forthcoming Mathigon advent calendar, which presents a puzzle a day from Dec 1 to 24.

Mathigon is a beautiful, incredibly engaging and free interactive website for the maths-curious. If you haven’t visited it before, I recommend a browse. And if you have, it’s worth a checking out again since new features are always coming online.

PLEASE NO SPOILERS

I’ll be back at 5pm UK with the solutions.

UPDATE: You can read the solutions here.

I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.

I give school talks about maths and puzzles (online and in person). If your school is interested please get in touch.