# Math puzzle driving me crazy **URL:** \ **Category:** Miscellaneous and Personal Stuff I Must Share\ **Created:** [August 11, 2006, 3:46pm UTC](https://boards.straightdope.com/t/math-puzzle-driving-me-crazy/368289 "2006-08-11T15:46:22Z")\ **Posts on this page:** 19\ **Page:** 2
**Author:** ![Stranger\_On\_A\_Train](https://avatars.discourse-cdn.com/v4/letter/s/13edae/32.png) [@Stranger\_On\_A\_Train](https://boards.straightdope.com/u/Stranger_On_A_Train)\ **Post date:** [August 11, 2006, 4:49pm UTC](https://boards.straightdope.com/t/math-puzzle-driving-me-crazy/368289/21 "2006-08-11T16:49:27Z")
Damnit, I should have previewed. Good work, **Straun**. Stranger ---
**Author:** ![Baron\_Greenback](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/baron_greenback/32/48_2.png) [@Baron\_Greenback](https://boards.straightdope.com/u/Baron_Greenback)\ **Post date:** [August 11, 2006, 6:06pm UTC](https://boards.straightdope.com/t/math-puzzle-driving-me-crazy/368289/22 "2006-08-11T18:06:28Z")
[QUOTE=twickster] So is someone going to cough up the $7 + $7 +$1 for **Struan** ’s membership? [/QUOTE] That’s a very kind thought, but I’ve just ponied up anyway. Let the search-a-thon begin!\* - well I’ll leave it until all the US folk are in bed. ---
**Author:** ![twickster](https://avatars.discourse-cdn.com/v4/letter/t/ec9cab/32.png) [@twickster](https://boards.straightdope.com/u/twickster)\ **Post date:** [August 11, 2006, 6:50pm UTC](https://boards.straightdope.com/t/math-puzzle-driving-me-crazy/368289/23 "2006-08-11T18:50:11Z")
[QUOTE=Struan] That’s a very kind thought, but I’ve just ponied up anyway.. [/QUOTE] Yay! Welcome! Since you’ve proven yourself worthy, we can do _either_ the goat _or_ the calamari for your initiation – what say you? ---
**Author:** ![gigi](https://avatars.discourse-cdn.com/v4/letter/g/a587f6/32.png) [@gigi](https://boards.straightdope.com/u/gigi)\ **Post date:** [August 11, 2006, 8:08pm UTC](https://boards.straightdope.com/t/math-puzzle-driving-me-crazy/368289/24 "2006-08-11T20:08:37Z")
[QUOTE=Struan] (7+7) \* (7+(1/7)) [/QUOTE] No way, that’s four 7s. Oh wait… ---
**Author:** ![Zebra](https://avatars.discourse-cdn.com/v4/letter/z/c0e974/32.png) [@Zebra](https://boards.straightdope.com/u/Zebra)\ **Post date:** [August 11, 2006, 8:36pm UTC](https://boards.straightdope.com/t/math-puzzle-driving-me-crazy/368289/25 "2006-08-11T20:36:06Z")
**Sturan** is the person that sent it to **jjimm** in the first place. Or (s)he is really smart. ---
**Author:** ![Stranger\_On\_A\_Train](https://avatars.discourse-cdn.com/v4/letter/s/13edae/32.png) [@Stranger\_On\_A\_Train](https://boards.straightdope.com/u/Stranger_On_A_Train)\ **Post date:** [August 11, 2006, 9:33pm UTC](https://boards.straightdope.com/t/math-puzzle-driving-me-crazy/368289/26 "2006-08-11T21:33:30Z")
[QUOTE=Zebra] **Sturan** is the person that sent it to **jjimm** in the first place…Or (s)he is really smart. [/QUOTE] Actually, it’s not that tough. Try this: (2)(50) = 100 (2)(49 + 1) = 100 ((7+7)/7) (7_7 + 1) = 100 Now multiply the first set of parentheses by 7 and divide the second set by 7, such that:7_((7+7)/7) (1/7)(7\*7 + 1) = 100 (7+7) (7 + 1/7) = 100 The trick is not minding that your answer involves a rational fraction that doesn’t reduce to an integer. Stranger ---
**Author:** ![Baron\_Greenback](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/baron_greenback/32/48_2.png) [@Baron\_Greenback](https://boards.straightdope.com/u/Baron_Greenback)\ **Post date:** [August 11, 2006, 10:18pm UTC](https://boards.straightdope.com/t/math-puzzle-driving-me-crazy/368289/27 "2006-08-11T22:18:33Z")
[QUOTE=Stranger On A Train] Actually, it’s not that tough. Try this: (2)(50) = 100 (2)(49 + 1) = 100 ((7+7)/7) (7_7 + 1) = 100 Now multiply the first set of parentheses by 7 and divide the second set by 7, such that:7_((7+7)/7) (1/7)(7\*7 + 1) = 100 (7+7) (7 + 1/7) = 100 The trick is not minding that your answer involves a rational fraction that doesn’t reduce to an integer. Stranger [/QUOTE] Ummm, that’s way overthinking compared to my process. Obviously there are two 49s available so only a further two is required. Given a one to play with, a fraction presents itself. Mind you I had to check it with calc. Oh, and if there’s any goat going about, could I have it curried please. ---
**Author:** ![Baron\_Greenback](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/baron_greenback/32/48_2.png) [@Baron\_Greenback](https://boards.straightdope.com/u/Baron_Greenback)\ **Post date:** [August 11, 2006, 10:25pm UTC](https://boards.straightdope.com/t/math-puzzle-driving-me-crazy/368289/28 "2006-08-11T22:25:40Z")
[QUOTE=Zebra] **Sturan** is the person that sent it to **jjimm** in the first place. Or (s)he is really smart. [/QUOTE] He! And it’s my real name too. Don’t worry about misspelling it, I’ve got used to it. It’s not a totally obscure name in these parts, but it isn’t an everyday one either. Straun, and gulp!!! Strewen are the ones I get most often. ---
**Author:** ![rowrrbazzle](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/rowrrbazzle/32/414_2.png) [@rowrrbazzle](https://boards.straightdope.com/u/rowrrbazzle)\ **Post date:** [August 11, 2006, 10:53pm UTC](https://boards.straightdope.com/t/math-puzzle-driving-me-crazy/368289/29 "2006-08-11T22:53:16Z")
```auto __ 77/.77 + 1 ``` (works for any digit) ---
**Author:** ![Baron\_Greenback](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/baron_greenback/32/48_2.png) [@Baron\_Greenback](https://boards.straightdope.com/u/Baron_Greenback)\ **Post date:** [August 11, 2006, 11:42pm UTC](https://boards.straightdope.com/t/math-puzzle-driving-me-crazy/368289/30 "2006-08-11T23:42:14Z")
[QUOTE=rowrrbazzle] ```auto __ 77/.77 + 1 ``` (works for any digit) [/QUOTE] How does that work? ---
**Author:** ![rowrrbazzle](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/rowrrbazzle/32/414_2.png) [@rowrrbazzle](https://boards.straightdope.com/u/rowrrbazzle)\ **Post date:** [August 12, 2006, 11:11pm UTC](https://boards.straightdope.com/t/math-puzzle-driving-me-crazy/368289/31 "2006-08-12T23:11:10Z")
The bar over the .77 indicates it repeats forever, giving it a value of 7/9. So ```auto __ xx/.xx = xx/(x/9) = xx*9/x = 11 * 9 = 99 ``` It would work for only 3 7s (or any digit) as well. The OP should send it back to the person he got it from as a return challenge. ---
**Author:** ![Baron\_Greenback](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/baron_greenback/32/48_2.png) [@Baron\_Greenback](https://boards.straightdope.com/u/Baron_Greenback)\ **Post date:** [August 12, 2006, 11:55pm UTC](https://boards.straightdope.com/t/math-puzzle-driving-me-crazy/368289/32 "2006-08-12T23:55:36Z")
Doesn’t your expression just tend towards 100, though? I mean it would always test as being less than 100? It might be one of those 2+2=5 for large values of 2 things, but I’ll cheerfully admit to not being able grasp much/any number theory stuff. God knows how I managed to get through my degree. ---
**Author:** ![don\_t\_ask](https://avatars.discourse-cdn.com/v4/letter/d/e68b1a/32.png) [@don\_t\_ask](https://boards.straightdope.com/u/don_t_ask)\ **Post date:** [August 13, 2006, 12:42am UTC](https://boards.straightdope.com/t/math-puzzle-driving-me-crazy/368289/33 "2006-08-13T00:42:23Z")
Thinking **any** mathematical operator was allowed I just instantly assumed 7[sup]2[/sup]+7[sup]2[/sup]+7/7+1 ---
**Author:** ![Antonius\_Block](https://avatars.discourse-cdn.com/v4/letter/a/51bf81/32.png) [@Antonius\_Block](https://boards.straightdope.com/u/Antonius_Block)\ **Post date:** [August 13, 2006, 12:53am UTC](https://boards.straightdope.com/t/math-puzzle-driving-me-crazy/368289/34 "2006-08-13T00:53:23Z")
[QUOTE=rowrrbazzle] ```auto __ 77/.77 + 1 ``` (works for any digit) [/QUOTE] Well, if you’re allowed to use decimal points, there’s a simpler solution: (77/.77)\*1=100 **Struan** , the whole “Does 0.999… =1” issue has has been addressed by [The Perfect Master](http://www.straightdope.com/columns/030711.html) and rehashed several times on the SDMB (such as [here](http://boards.straightdope.com/sdmb/showthread.php?t=196745) and [here](http://boards.straightdope.com/sdmb/showthread.php?t=242396)). At this point it’s pretty much axiomatic that they’re equal. _[Welcome to the Boards, but don’t even **think** of asking whether ducks’ quacks echo, where the missing dollars went in hotel transactions, the identity of the three words that end in -gry, or the origin of the phrase “The whole nine yards”.]_😉 ---
**Author:** ![ivylass](https://avatars.discourse-cdn.com/v4/letter/i/9de053/32.png) [@ivylass](https://boards.straightdope.com/u/ivylass)\ **Post date:** [August 13, 2006, 3:15am UTC](https://boards.straightdope.com/t/math-puzzle-driving-me-crazy/368289/35 "2006-08-13T03:15:50Z")
**Struan** , are you by chance a James Clavell fan? (I’m currently rereading _King Rat_.) ---
**Author:** ![MonkeyMensch](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@MonkeyMensch](https://boards.straightdope.com/u/MonkeyMensch)\ **Post date:** [August 13, 2006, 3:32am UTC](https://boards.straightdope.com/t/math-puzzle-driving-me-crazy/368289/36 "2006-08-13T03:32:34Z")
I was all ready to jump in with my trick solution but then saw the time of the OP. Oh well, I’ll throw it out there (and then you guys can throw it out.) 7\*7+7+7+1=100. It’s in octal, of course. 🙂 ---
**Author:** ![Baron\_Greenback](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/baron_greenback/32/48_2.png) [@Baron\_Greenback](https://boards.straightdope.com/u/Baron_Greenback)\ **Post date:** [August 13, 2006, 10:31am UTC](https://boards.straightdope.com/t/math-puzzle-driving-me-crazy/368289/37 "2006-08-13T10:31:24Z")
[QUOTE=ivylass] **Struan** , are you by chance a James Clavell fan? (I’m currently rereading _King Rat_.) [/QUOTE] No, Struan is my real-life first name. ---
**Author:** ![ivylass](https://avatars.discourse-cdn.com/v4/letter/i/9de053/32.png) [@ivylass](https://boards.straightdope.com/u/ivylass)\ **Post date:** [August 13, 2006, 7:46pm UTC](https://boards.straightdope.com/t/math-puzzle-driving-me-crazy/368289/38 "2006-08-13T19:46:39Z")
[QUOTE=Struan] No, Struan is my real-life first name. [/QUOTE] Okay…welcome aboard! ---
**Author:** ![panache45](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/panache45/32/64_2.png) [@panache45](https://boards.straightdope.com/u/panache45)\ **Post date:** [August 14, 2006, 5:47am UTC](https://boards.straightdope.com/t/math-puzzle-driving-me-crazy/368289/39 "2006-08-14T05:47:05Z")
[QUOTE=Thudlow Boink] Turn two of the 7s upside down so that they look like Ls. Then L + L + [(7/7) – 1] = 100. [/QUOTE] A variation on this one: Imagine the 7s are like in an LCD, with vertical right strokes. After you make the two Ls, take the remaining 7s, and place each one over an L, sliding it down to meet the L on its upper left and lower right. So what you have are two LCD 0s. Place them after the 1. [Previous page](https://boards.straightdope.com/t/math-puzzle-driving-me-crazy/368289.md?page=1)