0

I am not sure whether this is the correct forum. Anyway, here goes...

The game "Des chiffres et des lettres" is the most long living television game in French history; in its current form, it dates back as far as 1972.

There are two separate "minigames":

  • the longest word: given some random tiles drawn from either vowels or consonants, try and arrange those tiles to form a legal word (for some definition of "legal"; in France, that is a word defined in either of the two main reference dictionaires, Larousse and the Petit Robert);
  • the right count, which interests us here.

Rules of the right count:

  • you have 24 tiles: { 1..10 } x 2 (therefore 1, 1, 2, 2, etc), plus { 25, 50, 75, 100 };
  • you draw, randomly, 6 tiles from those 24;
  • you draw, randomly, a number between 100 and 999, included;
  • you may use any one tile zero or one time;
  • you may use the four basic operations that are addition, substraction, multiplication and division as long as an operation applied to any two numbers yields a strictly positive, integral number (so, for instance, 5 / 2 is not legal, nor is 2 - 3);
  • you may reuse the results of your intermediary operations, only once.

For instance, given:

7 1 2 3 6 8 | 199

a solution is:

  • 3 + 1 = 4;
  • 4 * 6 = 24;
  • 24 * 8 = 192;
  • 192 + 7 = 199.

One page, which I stumbled upon and unfortunately cannot find the link back right now, claimed that any such random draw has a 94% chance of success. Unfortunately, in additon to having lost the link to the page making this statement, my knowledge of math is too poor to prove or disprove such a claim.

Is there a method to compute such a proof or disproof at the very least?

fge
  • 139
  • While the rules seems clear enough to decide if a solution exists, I don't seem any shortcuts that allow the chance of success to be easily computed. You should probably begin by counting the possible "draws" and then decide whether evaluating all of them is worth your time. – hardmath Jul 18 '16 at 18:10
  • 1
    This is a game on the long-running TV programme Countdown on Channel 4 in the UK. On Countdown it's called the numbers game. There is some pertinent information here: http://legavrik.blogspot.co.uk/2014/04/countdown-probability-pt-2.html though, unfortunately, not an answer to the question you asked. – Rosie F Jul 18 '16 at 18:23
  • @RosieF Countdown is derived from "Des chiffres et des lettres", in fact. But the link you provided was unknown to me... Reading... – fge Jul 18 '16 at 18:34
  • @RosieF the link you provided is in fact an answer in itself! Its content is all I wanted to know, and more... – fge Jul 18 '16 at 20:42

0 Answers0