Can you solve it? The crossword that counts itself

Hello guzzlers.

First I’d like to introduce my friend Lee Sallows, who is a master at writing sentences that count the number of letters they contain. Like this classic:

This pangram contains four As, one B, two Cs, one D, thirty Es, six Fs, five Gs, seven Hs, eleven Is, one J, one K, two Ls, two Ms, eighteen Ns, fifteen Os, two Ps, one Q, five Rs, twenty-seven Ss, eighteen Ts, two Us, seven Vs, eight Ws, two Xs, three Ys, & one Z.

(A pangram is a sentence that contains every letter of the alphabet).

Sentences that count themselves like this are fiendish to construct and Lee has long wondered if one existed where the totals were described in percentages. Folks, the wait is over! Last week computer scientist Chris Patuzzo sent him this:

This sentence is dedicated to Lee Sallows and to within one decimal place four point five percent of the letters in this sentence are a’s, zero point one percent are b’s, four point three percent are c’s, zero point nine percent are d’s, twenty point one percent are e’s, one point five percent are f’s, zero point four percent are g’s, one point five percent are h’s, six point eight percent are i’s, zero point one percent are j’s, zero point one percent are k’s, one point one percent are l’s, zero point three percent are m’s, twelve point one percent are n’s, eight point one percent are o’s, seven point three percent are p’s, zero point one percent are q’s, nine point nine percent are r’s, five point six percent are s’s, nine point nine percent are t’s, zero point seven percent are u’s, one point four percent are v’s, zero point seven percent are w’s, zero point five percent are x’s, zero point three percent are y’s and one point six percent are z’s.



Bravo Chris!

Okay, so to today’s puzzle. It is devised by Lee Sallows and is a crossword that self-enumerates.

Each of the six vertical and six horizontal entries gives you the number of times a letter is used in the puzzle, and is of the form:

[NUMBER][SPACE][LETTER](S)

For example: “One Q”, “Five Ps”, “Ten Xs”, “Seventeen Es”.

In other words, every entry has a blank space after the number word and ends in an ‘s’ where there is a plural.

The rule is that each entry must accurately describe the completed puzzle. So, if the examples I just gave were correct then the completed puzzle would have a single Q, five Ps, ten Xs and seventeen Es.

Facebook Twitter Pinterest Fill in the gaps. (Except the space in each entry between the number word and the letter, of course). We’ve made the image printable. Photograph: Lee Sallows

Note that there are 12 unique entries, indicating that only 12 different letters are used in the completed grid.

It is possible to solve this puzzle using logic alone, and I’ll be back later today with just how to do it. (The solution post is now live: click here).

Facebook Twitter Pinterest Lee Sallows: elation in self-enumeration.

I post a puzzle here on a Monday every two weeks.

If puzzles make your brain hurt, and you want a less challenging mathematical activity, why not try my maths colouring book Snowflake Seashell Star, out this week in the US with the grander title, Patterns of the Universe.

I write about maths on my other Guardian blog, Adventures in Numberland. You can also check me out on Twitter, Facebook, Google+ and my personal website.

And if know of any great puzzles that you would like me to set here, get in touch.