Earlier at the moment I set you these 4 lexical-numerical puzzles, impressed by Tom Lehrer’s track That’s Arithmetic. Right here they’re once more with options. Additionally, you will uncover the highly-anticipated successful entry to the competitors for many good self-referential fraction.

1. Pair and share

The phrases ‘zero’ and ‘one’ share letters (‘e’ and ‘o’). The phrases ‘one’ and ‘two’ share a letter (‘o’), and the phrases ‘two’ and ‘three’ additionally share a letter (‘t’). How far do it’s important to depend in English to seek out two consecutive numbers which don’t share a letter in frequent?

Answer: Surprisingly there are NO consecutive numbers that don’t share letters in English. (Should you cant discover two non-sharing consecutive numbers beneath ten, the probabilities of discovering any above ten are going to be fairly low.) It will seem that English is uncommon on this regard – French, Spanish and German all have non-sharing consecutive numbers: deux/trois, siete/ocho and vier/fünf.

2. Spell it out!

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

What’s the lowest quantity to have this identical property, particularly that the variety of letters when written as a phrase equals the variety of digits when written in numerals?

Answer: ‘one billion’ has ten letters and 1,000,000,000 ten digits.

3. Satisfying sentence

“This sentence comprises _______ letters”

Write a quantity in phrases within the clean house within the above sentence that can make the assertion true.

Answer: ‘thirty six’ or ‘thirty eight’

4. Humorous fractions (and win a prize)

Within the phrase “two ninths”, the fraction of letters which might be vowels is 2 ninths. Discover another fractions which have comparable self-referential properties.

Answer I requested you to ship in strategies, and I promised I’d ship a replica of the e-book That’s Arithmetic to the one that got here up with one I favored essentially the most.

There have been many entries, and I beloved the creativity of all of them. Listed here are a number of the very best ones.

A number of folks tried to seek out methods to seize the truth that 22/7 is the very best easy approximation of pi. Of those

TWENTY TWO SEVENTHS ARE PI (7 vowels over 22 letters) from Andrew Brindle was the best.

Peter Taylor created this implausible sum of fractions:

ONE HALF PLUS ONE ELEVENTH (which equals 13/22, and has 13 consonants in 22 letters)

A reader known as Steve submitted THE SQUARE ROOT OF TWO THOUSAND ONE HUNDRED AND SIXTEEN, which is has 46 letters, and which describes the quantity 46. (Not a fraction, bit nonetheless good.)

Enjoyable, however a bit cumbersome is ONE HUNDRED AND THREE THREE HUNDRED AND NINTHS from Andy Knott, which has 13 vowels in 39 letters, and 103/309 = 1/3 = 13/39.

Eric Angelini (who wrote the second puzzle in at the moment’s column) got here up with ZERO POINT FOUR HUNDRED which has 8 vowels in 20 letters and is 0.400.

However my favorite got here in from Vanessa Walker:

ELEVEN SIXTEENTHS OF ELEVEN SIXTEENTHS ARE NOT E’S

Thanks for everybody’s entries, and sorry I used to be not capable of reply to you all personally.

{Photograph}: Mama Makes Books

Vanessa wins a replica of That’s Arithmetic, a kids’s e-book written by Chris Smith and impressed by the Tom Lehrer track of the identical identify.

I hope you loved at the moment’s puzzles. I’ll be again in two weeks.

I set a puzzle right here each two weeks on a Monday. I’m at all times on the look-out for excellent puzzles. If you need to counsel one, electronic mail me.

I give college talks about maths and puzzles (on-line and in individual). In case your college is please get in contact.