Can you solve it? That’s Mathematics!

Before we get to today’s puzzles, here is a curious fact I learned recently:

If you start with the word “YES” and advance each letter 16 along in the alphabet, it spells “OUI”?

Incroyable. I know. In this lexical-numerical spirit, all of todays puzzles are about number patterns in words.

1. Pair and share

The words ‘zero’ and ‘one’ share letters (‘e’ and ‘o’). The words ‘one’ and ‘two’ share a letter (‘o’), and the words ‘two’ and ‘three’ also share a letter (‘t’). How far do you have to count in English to find two consecutive numbers which don’t share a letter in common?

2. Spell it out!

‘Eleven trillion’ has an interesting property. It consists of 14 letters and when written out is 11,000,000,000,000, which consists of 14 numbers.

What is the lowest number to have this same property, namely that the number of letters when written as a word equals the number of digits when written in numerals?

3. Satisfying sentence

“This sentence contains _______ letters”

Write a number in words in the blank space in the above sentence that will make the statement true.

4. Funny fractions (and win a prize)

In the phrase “two ninths”, the fraction of letters that are vowels is two ninths. Find some other fractions that have similar self-referential properties.

Be creative! You could win a prize!

I have a copy of a new book, That’s Mathematics, and I will send it to the person who sends me the self-referential fraction I like the most.

The book was written by Chris Smith, Scotland’s number one maths teacher, as a tribute to the mathematician and songwriter Tom Lehrer, who is famously as playful with words as he is with numbers.

Back in in 2000, during the Covid lockdown, Chris and two maths teacher pals Ed Southall and Ben Sparks decided to adapt Lehrer’s song That’s Mathematics and ask maths popularisers from around the world to sing a line from it. They edited the contributions together and the video – featuring Hannah Fry, Bobby Seagull, Rachel Riley, Vsauce, Eddie Woo and more – registered more that half a million views. Shortly afterward, a publisher approached Smith asking him if he wanted to turn the song into a children’s book. He did, and the book is out on March 1 in the UK.

It was Chris who alerted me to the fact about YES and OUI , and he also suggested puzzles 1, 3 and 4. (Puzzle 2 is from Eric Angelini).

Ill be back at 5pm UK with the solutions and the winner.

PLEASE NO SPOILERS. Instead discuss your favourite Tom Lehrer songs and cover versions.

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.

Finally, if you want to see That’s Mathematics sung by 22 maths popularisers (including me) here it is:

That’s Mathematics by Chris Smith based on words by Tom Lehrer is out on March 1. You can preorder here.