# "Le compte est bon", or, anyone for a math game? **URL:** \ **Category:** The Game Room\ **Created:** [January 12, 2010, 11:59pm UTC](https://boards.straightdope.com/t/le-compte-est-bon-or-anyone-for-a-math-game/524727 "2010-01-12T23:59:23Z")\ **Posts on this page:** 20\ **Page:** 3
**Author:** ![Arnold\_Winkelried](https://avatars.discourse-cdn.com/v4/letter/a/3d9bf3/32.png) [@Arnold\_Winkelried](https://boards.straightdope.com/u/Arnold_Winkelried)\ **Post date:** [January 19, 2010, 1:16am UTC](https://boards.straightdope.com/t/le-compte-est-bon-or-anyone-for-a-math-game/524727/41 "2010-01-19T01:16:08Z")
(25 + 1) \* (10 + 7) + 5 = 447 is the best I can do ---
**Author:** ![Quartz](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/quartz/32/267_2.png) [@Quartz](https://boards.straightdope.com/u/Quartz)\ **Post date:** [January 19, 2010, 8:32am UTC](https://boards.straightdope.com/t/le-compte-est-bon-or-anyone-for-a-math-game/524727/42 "2010-01-19T08:32:09Z")
448 = (25 + 7) \* (10 + 5 - 1) Next up: 2, 4, 7, 9, 10, 25. Target is 881 ---
**Author:** ![Tom\_Scud](https://avatars.discourse-cdn.com/v4/letter/t/f08c70/32.png) [@Tom\_Scud](https://boards.straightdope.com/u/Tom_Scud)\ **Post date:** [January 19, 2010, 1:32pm UTC](https://boards.straightdope.com/t/le-compte-est-bon-or-anyone-for-a-math-game/524727/43 "2010-01-19T13:32:58Z")
> [@Quartz](#): > > 448 = (25 + 7) \* (10 + 5 - 1) > > Next up: 2, 4, 7, 9, 10, 25. Target is 881 9 x 4 x 25 - (10 + 7 + 2) 1, 1, 3, 3, 7, 7. Target 500. ---
**Author:** ![Arnold\_Winkelried](https://avatars.discourse-cdn.com/v4/letter/a/3d9bf3/32.png) [@Arnold\_Winkelried](https://boards.straightdope.com/u/Arnold_Winkelried)\ **Post date:** [January 19, 2010, 1:53pm UTC](https://boards.straightdope.com/t/le-compte-est-bon-or-anyone-for-a-math-game/524727/44 "2010-01-19T13:53:02Z")
Maybe I’m confused, but isn’t this the best possible? (7 × 7 × 3 × 3) + 1 + 1 = 443 ---
**Author:** ![Tom\_Scud](https://avatars.discourse-cdn.com/v4/letter/t/f08c70/32.png) [@Tom\_Scud](https://boards.straightdope.com/u/Tom_Scud)\ **Post date:** [January 19, 2010, 2:41pm UTC](https://boards.straightdope.com/t/le-compte-est-bon-or-anyone-for-a-math-game/524727/45 "2010-01-19T14:41:39Z")
> [@Arnold\_Winkelried](#): > > Maybe I’m confused, but isn’t this the best possible? > (7 × 7 × 3 × 3) + 1 + 1 = 443 Nope. It’s solvable. ---
**Author:** ![Quartz](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/quartz/32/267_2.png) [@Quartz](https://boards.straightdope.com/u/Quartz)\ **Post date:** [January 19, 2010, 3:40pm UTC](https://boards.straightdope.com/t/le-compte-est-bon-or-anyone-for-a-math-game/524727/46 "2010-01-19T15:40:49Z")
> [@Arnold\_Winkelried](#): > > Maybe I’m confused, but isn’t this the best possible? > (7 × 7 × 3 × 3) + 1 + 1 = 443 No. Max is (9 + 1 + 1) x 7 x 3 x 3 = 77 x 9 = 693 This is easier than some of the earlier ones. ((3 x 3) + 1) x ((7 x 7) + 1) = 500 Next up! The target is 951 and the numbers are 2 2 5 6 25 75 ---
**Author:** ![Tom\_Scud](https://avatars.discourse-cdn.com/v4/letter/t/f08c70/32.png) [@Tom\_Scud](https://boards.straightdope.com/u/Tom_Scud)\ **Post date:** [January 19, 2010, 3:59pm UTC](https://boards.straightdope.com/t/le-compte-est-bon-or-anyone-for-a-math-game/524727/47 "2010-01-19T15:59:45Z")
> [@Quartz](#): > > No. Max is (9 + 1 + 1) x 7 x 3 x 3 = 77 x 9 = 693 Technically, I think the max is 7 x 7 x (3+1) x (3+1) = 784. But anyway. ---
**Author:** ![Dead\_Cat](https://avatars.discourse-cdn.com/v4/letter/d/9fc29f/32.png) [@Dead\_Cat](https://boards.straightdope.com/u/Dead_Cat)\ **Post date:** [January 19, 2010, 6:20pm UTC](https://boards.straightdope.com/t/le-compte-est-bon-or-anyone-for-a-math-game/524727/48 "2010-01-19T18:20:27Z")
> [@Quartz](#): > > The target is 951 and the numbers are 2 2 5 6 25 75 ((2 x 6) x (75 + 2)) + 25 = 949. Alternatively, ((5 + 6 + 2) x 75) - 25 = 950. But I can’t get 951. > [@Tom\_Scud](#): > > Technically, I think the max is 7 x 7 x (3+1) x (3+1) = 784. But anyway. Does anyone know an algorithm for finding the maximum total of 6 numbers using just multiplication and addition? ---
**Author:** ![Quartz](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/quartz/32/267_2.png) [@Quartz](https://boards.straightdope.com/u/Quartz)\ **Post date:** [January 19, 2010, 6:40pm UTC](https://boards.straightdope.com/t/le-compte-est-bon-or-anyone-for-a-math-game/524727/49 "2010-01-19T18:40:00Z")
I should note that I do not know if this one is solvable. I gave it a quick try to ensure that the solution wasn’t trivial. ---
**Author:** ![Tom\_Scud](https://avatars.discourse-cdn.com/v4/letter/t/f08c70/32.png) [@Tom\_Scud](https://boards.straightdope.com/u/Tom_Scud)\ **Post date:** [January 19, 2010, 6:47pm UTC](https://boards.straightdope.com/t/le-compte-est-bon-or-anyone-for-a-math-game/524727/50 "2010-01-19T18:47:18Z")
> [@Dead\_Cat](#): > > ((2 x 6) x (75 + 2)) + 25 = 949. Alternatively, ((5 + 6 + 2) x 75) - 25 = 950. But I can’t get 951. I can’t get 951 either. (75 x 25 + 5)/2 + (6 x 2) = 952, for the sake of completeness. > [@](#): > > Does anyone know an algorithm for finding the maximum total of 6 numbers using just multiplication and addition? Pretty simple (assuming the set we have to work with) - first add any 1s to the lowest non-1 numbers, then multiply all the numbers by each other. Come to think, actually (1+1) x 3 x 3 x 7 x 7 = 882, so in fact if there are 2 1’s you should add them to make a 2 then multiply out; if there’s only one 1 you should add it to the otherwise-lowest number and then multiply. ---
**Author:** ![Duke](https://avatars.discourse-cdn.com/v4/letter/d/e8c25b/32.png) [@Duke](https://boards.straightdope.com/u/Duke)\ **Post date:** [January 19, 2010, 7:04pm UTC](https://boards.straightdope.com/t/le-compte-est-bon-or-anyone-for-a-math-game/524727/51 "2010-01-19T19:04:39Z")
> [@Dead\_Cat](#): > > Working numbers: 1, 1, 2, 2, 3, 3. > Target number: 999. ((3\*2) + 2 + 1 +1)^3 = 1000. Wait, that was cheating. ---
**Author:** ![Giles](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/giles/32/60_2.png) [@Giles](https://boards.straightdope.com/u/Giles)\ **Post date:** [January 19, 2010, 7:07pm UTC](https://boards.straightdope.com/t/le-compte-est-bon-or-anyone-for-a-math-game/524727/52 "2010-01-19T19:07:23Z")
> [@Tom\_Scud](#): > > … if there are 2 1’s you should add them to make a 2 then multiply out; if there’s only one 1 you should add it to the otherwise-lowest number and then multiply. If the rules allow three or more 1’s, then I think the rule would be to add them in groups of three until you have two, three or four left. Then: With two left, group as (1+1+1)_…_(1+1+1)_(1+1)_… With three left, group as (1+1+1)_…_(1+1+1)_(1+1+1)_… With four left, group as (1+1+1)_…_(1+1+1)_(1+n)_… (where n is the smallest number apart from 1) ---
**Author:** ![Quartz](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/quartz/32/267_2.png) [@Quartz](https://boards.straightdope.com/u/Quartz)\ **Post date:** [January 19, 2010, 7:16pm UTC](https://boards.straightdope.com/t/le-compte-est-bon-or-anyone-for-a-math-game/524727/53 "2010-01-19T19:16:24Z")
> [@Tom\_Scud](#): > > Technically, I think the max is 7 x 7 x (3+1) x (3+1) = 784. But anyway. :smack::smack: I’m not sure where I got the 9 from. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [January 19, 2010, 9:06pm UTC](https://boards.straightdope.com/t/le-compte-est-bon-or-anyone-for-a-math-game/524727/54 "2010-01-19T21:06:10Z")
> [@Duke](#): > > ((3\*2) + 2 + 1 +1)^3 = 1000. > > Wait, that was cheating. Well, if we allow exponents I can do you one better: ((2^3)+2)^3 -1 = 999, our target edit: or ((3^2)+1)^3 -1 = 999 ---
**Author:** ![Arnold\_Winkelried](https://avatars.discourse-cdn.com/v4/letter/a/3d9bf3/32.png) [@Arnold\_Winkelried](https://boards.straightdope.com/u/Arnold_Winkelried)\ **Post date:** [January 19, 2010, 10:44pm UTC](https://boards.straightdope.com/t/le-compte-est-bon-or-anyone-for-a-math-game/524727/55 "2010-01-19T22:44:34Z")
It appears to me that Dead Cat has come in first with a close answer to the last puzzle, and it also appears to me that I am arithmetically inept (see posts 44, 46, 47). If we allowed exponents, who knows what heights we could reach! ---
**Author:** ![Arnold\_Winkelried](https://avatars.discourse-cdn.com/v4/letter/a/3d9bf3/32.png) [@Arnold\_Winkelried](https://boards.straightdope.com/u/Arnold_Winkelried)\ **Post date:** [January 19, 2010, 10:46pm UTC](https://boards.straightdope.com/t/le-compte-est-bon-or-anyone-for-a-math-game/524727/56 "2010-01-19T22:46:46Z")
> [@Chronos](#): > > That depends on how big your numbers are. Over the domain of all numbers, puzzles with exact solutions are an infinitesimally small set compared to the ones without. True, but I am wondering, if you use the rules of the OP, how many of the possible puzzles disallow an “exact” answer. Quartz’s last puzzle _The target is 951 and the numbers are 2 2 5 6 25 75_ might be one of them. ---
**Author:** ![Red\_Skeezix](https://avatars.discourse-cdn.com/v4/letter/r/aca169/32.png) [@Red\_Skeezix](https://boards.straightdope.com/u/Red_Skeezix)\ **Post date:** [January 20, 2010, 5:14am UTC](https://boards.straightdope.com/t/le-compte-est-bon-or-anyone-for-a-math-game/524727/57 "2010-01-20T05:14:34Z")
951 = ((75 + 6 - 5)\*25 +2) /2 Target: 901 Numbers: 2,2,4,25,50,100 ---
**Author:** ![Kobal2](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kobal2/32/20_2.png) [@Kobal2](https://boards.straightdope.com/u/Kobal2)\ **Post date:** [January 20, 2010, 10:07am UTC](https://boards.straightdope.com/t/le-compte-est-bon-or-anyone-for-a-math-game/524727/58 "2010-01-20T10:07:37Z")
> [@Red\_Skeezix](#): > > Target: 901 > Numbers: 2,2,4,25,50,100 4\*50 _2_2 + 100 = 900. Don’t see a way to get that sodding 1. If I win anyway : Target : 557 Numbers : 1,3,6,9,10,100 ---
**Author:** ![Dead\_Cat](https://avatars.discourse-cdn.com/v4/letter/d/9fc29f/32.png) [@Dead\_Cat](https://boards.straightdope.com/u/Dead_Cat)\ **Post date:** [January 20, 2010, 2:03pm UTC](https://boards.straightdope.com/t/le-compte-est-bon-or-anyone-for-a-math-game/524727/59 "2010-01-20T14:03:23Z")
> [@Kobal2](#): > > 4\*50 _2_2 + 100 = 900. Don’t see a way to get that sodding 1. > > If I win anyway : > Target : 557 > Numbers : 1,3,6,9,10,100 I think you probably will, based on previous posts it’s probably solvable, but I can’t do it. (100 x (6 - 1)) + ((10 + 9) x 3) = 557. New target: 484 Numbers: 1, 2, 5, 7, 9, 9. Don’t know if this is solvable (or trivial). ---
**Author:** ![Tom\_Scud](https://avatars.discourse-cdn.com/v4/letter/t/f08c70/32.png) [@Tom\_Scud](https://boards.straightdope.com/u/Tom_Scud)\ **Post date:** [January 20, 2010, 2:46pm UTC](https://boards.straightdope.com/t/le-compte-est-bon-or-anyone-for-a-math-game/524727/60 "2010-01-20T14:46:30Z")
> [@Dead\_Cat](#): > > I think you probably will, based on previous posts it’s probably solvable, but I can’t do it. > > (100 x (6 - 1)) + ((10 + 9) x 3) = 557. > > New target: 484 > Numbers: 1, 2, 5, 7, 9, 9. > > Don’t know if this is solvable (or trivial). Not trivial anyway 9 x 9 x (5 + 1) - 2 = 484 5, 5, 10, 10, 25, 50 target 373 [Previous page](https://boards.straightdope.com/t/le-compte-est-bon-or-anyone-for-a-math-game/524727.md?page=2) [Next page](https://boards.straightdope.com/t/le-compte-est-bon-or-anyone-for-a-math-game/524727.md?page=4)