Before we get to today’s riddles, here’s a curious fact I learned recently:
If you start with the word “YES” and advance each letter by 16 in the alphabet, does that spell “YES”?
Amazing. I know. In this lexico-numerical spirit, all of today’s 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 that have no letter in common?
2. Spell it!
‘Eleven trillion’ has an interesting property. It consists of 14 letters and when written is 11,000,000,000,000, which consists of 14 digits.
What is the smallest number to have this same property, that the number of letters when written as a word is equal to the number of digits when written as digits?
3. Satisfactory sentence
“This sentence contains _______ letters”
Write a number in words in the blank space of the sentence above that will make the statement true.
4. Fun fractions (and win a prize)
In the phrase “two ninths”, the fraction of letters that are vowels is two ninths. Find other fractions that have similar self-referential properties.
Be creative! You could win a prize!
I have a copy of a new book, It’s math, and I will send it to the person who will send me the self-referential fraction that I like the most.
The book was written by Chris Smith, Scotland’s number one maths teacher, as a tribute to mathematician and songwriter Tom Lehrer, who was known to be as playful with words as he was with numbers.
Back in 2000, during the Covid lockdown, Chris and two math teacher buddies Ed Southall and Ben Sparks decided to adapt Lehrer’s song It’s math and ask math popularizers 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 many more – scored over half a million views. Soon after, a publisher approached Smith asking if he wanted to turn the song into a children’s book. He did, and the book was released on March 1 in the UK.
It was Chris who alerted me to YES and OUI, and he also suggested puzzles 1, 3, and 4. (Puzzle 2 is by Eric Angelini).
I’ll be back at 5pm in the UK with the solutions and the winner.
PLEASE NO SPOILERS. Instead, chat about your favorite Tom Lehrer songs and covers.
I install a puzzle here every two weeks on a Monday. I’m always on the lookout for great puzzles. If you want to suggest one, write to me.
I give school lectures on math and puzzles (online and in person). If your school is interested, please contact us.
Finally, if you want to see That’s Mathematics sung by 22 math popularizers (including me) it’s here:
It’s math by Chris Smith based on lyrics by Tom Lehrer will be released on March 1. You can pre-order here.