# Did you clear up it? Which is Arithmetic!

Before right now I established you these four lexical-numerical puzzles, inspired by Tom Lehrer’s music That’s Mathematics. Below they are once more with answers. You will also find the highly-expected winning entry to the level of competition for most outstanding self-referential fraction.

1. Pair and share

The words ‘zero’ and ‘one’ share letters (‘e’ and ‘o’). The terms ‘one’ and ‘two’ share a letter (‘o’), and the words and phrases ‘two’ and ‘three’ also share a letter (‘t’). How significantly do you have to rely in English to come across two consecutive numbers which do not share a letter in typical?

Answer: Amazingly there are NO consecutive numbers that really do not share letters in English. (If you cant obtain two non-sharing consecutive figures under 10, the odds of locating any previously mentioned 10 are going to be rather reduced.) It would appear that English is strange in this regard – French, Spanish and German all have non-sharing consecutive quantities: deux/trois, siete/ocho and vier/fünf.

2. Spell it out!

‘Eleven trillion’ has an interesting property. It is made up of 14 letters and when written out is 11,000,000,000,000, which is composed of 14 digits.

What is the cheapest selection to have this exact house, namely that the quantity of letters when composed as a term equals the range of digits when written in numerals?

Option: ‘one billion’ has ten letters and 1,000,000 10 digits.

3. Fulfilling sentence

“This sentence contains _______ letters”

Publish a amount in phrases in the blank place in the previously mentioned sentence that will make the assertion genuine.

Answer: ‘thirty six’ or ‘thirty eight’

4. Humorous fractions (and gain a prize)

In the phrase “two ninths”, the portion of letters that are vowels is two ninths. Obtain some other fractions that have equivalent self-referential houses.

Answer I questioned you to ship in suggestions, and I promised I would deliver a duplicate of the book Which is Mathematics to the individual who arrived up with just one I liked the most.

There ended up a lot of entries, and I loved the creative imagination of all of them. Right here are a assortment of the greatest kinds.

A number of individuals tried using to locate ways to capture the actuality that 22/7 is the greatest straightforward approximation of pi. Of these

20 TWO SEVENTHS ARE PI (7 vowels more than 22 letters) from Andrew Brindle was the neatest.

Peter Taylor established this fantastic sum of fractions:

A single Fifty percent Moreover A single ELEVENTH (which equals 13/22, and has 13 consonants in 22 letters)

A reader named Steve submitted THE Sq. ROOT OF TWO THOUSAND 1 HUNDRED AND SIXTEEN, which is has 46 letters, and which describes the quantity 46. (Not a fraction, little bit nonetheless wonderful.)

Fun, but a bit cumbersome is A person 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 2nd puzzle in today’s column) arrived up with ZERO Point Four HUNDRED which has 8 vowels in 20 letters and is .400.

But my favorite came in from Vanessa Walker:

ELEVEN SIXTEENTHS OF ELEVEN SIXTEENTHS ARE NOT E’S

Thanks for everyone’s entries, and sorry I was not in a position to reply to you all personally.

Vanessa wins a copy of Which is Mathematics, a children’s guide written by Chris Smith and influenced by the Tom Lehrer track of the identical name.

I hope you loved today’s puzzles. I’ll be again in two months.

I set a puzzle in this article just about every two months on a Monday. I’m often on the glance-out for good puzzles. If you would like to propose one particular, e mail me.

I give college talks about maths and puzzles (on the web and in person). If your college is fascinated remember to get in contact.