A regular tetrahedron is constructed within a unit cube in such a way that its four vertices coincide with those of the cube – see the diagram.

**Question Alpha**

What is the volume of the tetrahedron?

**Question Omega**

If you have been following this week’s questions, then you’ll find the above pretty simple. So, let’s increase the difficulty dial! Imagine constructing another regular tetrahedron using the other four vertices of the unit cube. The space where the two tetrahedra overlap is known as the core. What is the name of the polyhedral core? What is the volume of this core?

You may submit at least one answer to enter the competition.

Enjoy!

**You may discuss the question below, but no full answers, please, until the competition has closed!**

**You can receive these questions directly to your email box or read them in an RSS reader. Subscribe using the links on the right.**

**If you would like to DONATE PRIZES for the next PMQ, send me a message here.**

**How to Enter****Send your complete solution by email to pmq16euclid@giftedmaths.com.**This email address shall be removed after the competition closes to avoid spam.

**This PMQ16 competition closes on MONDAY 29 April at 23:59 GMT - one extra weekday from now on**.

**The Prize****The prizes for this PMQ are 3 free places in our Online Maths Club for 3 months.**The very first correct solution will receive a prize plus two others randomly selected from all the other correct answers. The email time stamp shall determine the order of entries received. All winners can have their name posted and a link to their own online profile at their favourite social network or their own blog.

**Quick Rules****Look at the expanded rules on our PMQ page.**

Anybody can enter our Prize Maths Quiz; adults and students.

Use the official server clock in the right column to avoid late entries.

All emails and email addresses sent to us will be deleted after the winners have been processed.

DO NOT submit your entries to the comments section at the bottom of this post.

You CAN discuss it there but you must email us to enter the competition.

We adhere to COPPA guidelines regarding children's online safety and security.

Enjoy the challenge!

**Send us your solution! You can't win if you don't participate.**

Then tell your friends!

## No comments:

## Post a Comment