# "Le compte est bon", or, anyone for a math game?

[post=11986491]My post here[/post] inspired me to propose this math game.

I used to watch a French game show called “Numbers and Letters”. One of the challenges in the game was called “The count is right” - you are given certain numbers and through four arithmetic operations (subtraction, addition, division, multiplication) you try to come as close as possible to a target number.

Rules
[list=A][li]Take 6 (working) numbers at random from the following set: 1 through 10, 25, 50, 75, 100 (each number from 1 to 10 can appear up to two times in your set of 6 - pretend you are drawing from a set of tiles like this: 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 25, 50, 75, 100)[/li][li]Pick a (target) number at random between 100 and 999[/li][li]Using +, −, ×, ÷ and the working numbers drawn in step A, try to get as close as possible to the target number drawn in step B[/li][/list]

In this medium, I propose that it would work this way:
[ol]
[li]Someone proposes a challenge[/li][li]The winner is the first poster to get exactly the target number from the working numbers[/li]OR
the person with the closest result in the first 5 posts following the challenge (in case there is no exact solution)
[li]Winner proposes a new challenge[/li][li]The person proposing the challenge doesn’t get to try to solve their own challenge[/li][/ol]

Example
working numbers 3, 75, 2, 4, 1, 1
target number 888
75 - 1 = 74
3 × 4 = 12
74 × 12 = 888
First challenge
working numbers 9, 75, 8, 3, 8, 2
target number 798
P.S. If someone knows of an existing application (e.g. a web form) that solves these types of problem, please let me know, then the game would become kind of pointless unless the participants promise not to use the automated solver.

75x9+8x8=739

988+75*3-2

799

I just realized that one of the things that made this workable on the TV show is the time limit.
In this case, I really doubt anyone can come closer than pulykamell. Well done!

( I was trying to use an 8 * 100 idea as a starting point but the closest I came was (75 / 3) * (8 / 2) * 8 = 800 )

So I will declare pulykamell the winner and modify the rules to say “best guess in the next 5 posts or in the next 4 hours” - unless someone has a better timeframe to suggest.

pulykamell, do you have a challenge?

ETA: in the game a solution is “better” if it uses less of the working numbers. So if the target number is 567, and someone reaches 565 using 5 working numbers, and another person reaches 569 using 4 working numbers, the second person is the winner: both are off by 2 but the second person did it using less working numbers.

Sure, here we go:

Second challenge

working numbers: 1,3,4,7,7,25
target number: 233

(7 + 3 - 1) * 25 + 7 = 232

I couldn’t solve this one myself, so I checked it out and it is solvable. If no body guesses it I’ll give the answer after the closest is decided upon.

Also the answer to the first one is:
798= (2+8)89+3+75

working numbers: 1,3,4,7,7,25
target number: 233

((7 +4)* 3 )+(1+7)*25 = 233 I think.

New challenge.

working numbers: 3,3,5,7,8,25
target number: 342

working numbers: 3,3,5,7,8,25
target number: 342

(25 + 5 + 8) *3 *3 = 342

New Challenge:

Working: 2,4,25,6,7,10
target: 658

4*(25+2)*6 + 10 = 658

Working numbers : 5, 3, 75, 1, 1, 9
Target number : 246

3*(75+9-1-1) = 246

New Challenge:

Working numbers: 1, 3, 10, 25, 75, 100
Target number: 737

Too easy! 75 - 1 = 74. 74 x 10 = 740. 740 - 3 = 737.

New challenge:

Working numbers: 1, 1, 2, 2, 3, 3.
Target number: 999.

Good luck!

OK, I kid. How about:

Working numbers: 1, 7, 5, 4, 2, 50.
Target number: 477.

By the way, I know this game from the British TV programme Countdown, which is almost certainly the UK’s longest-running gameshow, with 27 unbroken years and counting. Apparently, the UK version was based on the French program Des chiffres et des lettres that the OP refers to.

This is similar to the card game Krypto. There is a solver application here, but it calls for 5 “working numbers,” not 6.

((50*2)+1)5-(74) = 477

How about:
Working numbers: 3, 4, 5, 6, 7, 8, 75
Target: 491

Boy, you people are good! There must be some cases where it can’t be solved exactly. At least on the TV show this happened (of course the people on the TV show had a time limit).

How did you “check it out”?

(75 * 6) + (8 * 5) + 4 - 3 = 491

Very good, even though it’s not the solution I had in mind:

3456 + 78 + 75 = 491