# Challenge 24 **URL:** \ **Category:** Miscellaneous and Personal Stuff I Must Share\ **Created:** [April 23, 2004, 11:22pm UTC](https://boards.straightdope.com/t/challenge-24/241726 "2004-04-23T23:22:34Z")\ **Posts on this page:** 18\ **Page:** 1
**Author:** ![Captain\_Carrot](https://avatars.discourse-cdn.com/v4/letter/c/f0a364/32.png) [@Captain\_Carrot](https://boards.straightdope.com/u/Captain_Carrot)\ **Post date:** [April 23, 2004, 11:22pm UTC](https://boards.straightdope.com/t/challenge-24/241726/1 "2004-04-23T23:22:34Z")
There is a game (sort of) called Challenge 24. Basically, you get 4 numbers that you must make equal 24, using each one only once, and only using +, -, /, and \*, the four basic operations: Poster 1: 3, 6, 1/4, 3. Poster 2: (6/3)\*(3/(1/4))=24 ``` 5, 7, 1/8, 2/3 etc. ``` First four:10, 7, 6, 2. ---
**Author:** ![Kluge](https://avatars.discourse-cdn.com/v4/letter/k/a183cd/32.png) [@Kluge](https://boards.straightdope.com/u/Kluge)\ **Post date:** [April 24, 2004, 3:03am UTC](https://boards.straightdope.com/t/challenge-24/241726/2 "2004-04-24T03:03:33Z")
Wonderful game. Brings back good memories. A little to easy if you aren’t in direct timed competition though. Anyways… (10 - 7) \* (6 + 2) = 24 And I’ll contribute: 5, 23, 7, 6 ---
**Author:** ![SpasmicChaos](https://avatars.discourse-cdn.com/v4/letter/s/a698b9/32.png) [@SpasmicChaos](https://boards.straightdope.com/u/SpasmicChaos)\ **Post date:** [April 24, 2004, 3:30am UTC](https://boards.straightdope.com/t/challenge-24/241726/3 "2004-04-24T03:30:16Z")
7 \* 6 + 5 - 23 = 24 Next up: 13, 3, 1, 9 ---
**Author:** ![Odinoneeye](https://avatars.discourse-cdn.com/v4/letter/o/97f17d/32.png) [@Odinoneeye](https://boards.straightdope.com/u/Odinoneeye)\ **Post date:** [April 24, 2004, 3:53am UTC](https://boards.straightdope.com/t/challenge-24/241726/4 "2004-04-24T03:53:51Z")
13+3+9-1=24 27, 2, 9, 16 ---
**Author:** ![Hal\_Briston](https://avatars.discourse-cdn.com/v4/letter/h/a9a28c/32.png) [@Hal\_Briston](https://boards.straightdope.com/u/Hal_Briston)\ **Post date:** [April 24, 2004, 3:54am UTC](https://boards.straightdope.com/t/challenge-24/241726/5 "2004-04-24T03:54:39Z")
13 + 3 + 9 - 1 = 24 Interesting… Here ya go: 2 3/4, 2, 9, 6 ---
**Author:** ![Kluge](https://avatars.discourse-cdn.com/v4/letter/k/a183cd/32.png) [@Kluge](https://boards.straightdope.com/u/Kluge)\ **Post date:** [April 24, 2004, 3:59am UTC](https://boards.straightdope.com/t/challenge-24/241726/6 "2004-04-24T03:59:05Z")
Er, two? Odinoneeye: (27 / 9) \* (16 / 2) = 24 Hal Briston: 2.75 \* 2 \* 6 - 9 And the new on is: 12, 9, 7, 5 ---
**Author:** ![Captain\_Carrot](https://avatars.discourse-cdn.com/v4/letter/c/f0a364/32.png) [@Captain\_Carrot](https://boards.straightdope.com/u/Captain_Carrot)\ **Post date:** [April 25, 2004, 6:10pm UTC](https://boards.straightdope.com/t/challenge-24/241726/7 "2004-04-25T18:10:03Z")
And you thought this would be too easy, **Kluge**. If it proves to be too easy, we can always change the rules slightly. I’m surprised the math guys aren’t in here, though… This sort of thing should be right up their alley. Anyway, 7\*5-12-9=24. That took me so long to figure out. I spent about half an hour on it and gave up, and the answer came to me while this reply page was loading. (Who else misses the old format with the reply box at the bottom of the thread?) 3, 5, 2, 6 ---
**Author:** ![Critical\_Mass](https://avatars.discourse-cdn.com/v4/letter/c/f1d935/32.png) [@Critical\_Mass](https://boards.straightdope.com/u/Critical_Mass)\ **Post date:** [April 25, 2004, 7:29pm UTC](https://boards.straightdope.com/t/challenge-24/241726/8 "2004-04-25T19:29:12Z")
I keep looking at 7\*5-12-9 and coming up with 14 3_5_2-6=24 How about 21,6,8,2 ---
**Author:** ![MaxTheVool](https://avatars.discourse-cdn.com/v4/letter/m/9fc29f/32.png) [@MaxTheVool](https://boards.straightdope.com/u/MaxTheVool)\ **Post date:** [April 25, 2004, 11:16pm UTC](https://boards.straightdope.com/t/challenge-24/241726/9 "2004-04-25T23:16:56Z")
21 + 6 / (sqrt(8 / 2)) 7, 9, 11, 4.5 ---
**Author:** ![MaxTheVool](https://avatars.discourse-cdn.com/v4/letter/m/9fc29f/32.png) [@MaxTheVool](https://boards.straightdope.com/u/MaxTheVool)\ **Post date:** [April 25, 2004, 11:31pm UTC](https://boards.straightdope.com/t/challenge-24/241726/10 "2004-04-25T23:31:00Z")
Whoops, I didn’t see that the rules specified only ±\*/. That makes it a lot harder, and I can’t find a solution for 21, 6, 8, 2 at all. (Although if we’re allowed to use “ln” to mean log-base-2, there’s 21 \* 2 - 6 \* ln(8) ) ---
**Author:** ![Critical\_Mass](https://avatars.discourse-cdn.com/v4/letter/c/f1d935/32.png) [@Critical\_Mass](https://boards.straightdope.com/u/Critical_Mass)\ **Post date:** [April 26, 2004, 12:38am UTC](https://boards.straightdope.com/t/challenge-24/241726/11 "2004-04-26T00:38:17Z")
> [@MaxTheVool](#): > > I can’t find a solution for 21, 6, 8, 2 at all. > > (Although if we’re allowed to use “ln” to mean log-base-2, there’s 21 \* 2 - 6 \* ln(8) ) Didn’t mean to come up with a show stopper. My Bad. I just chose some random numbers. Do I win something? 🙂 In order to get thinkgs back on track, how about: 2 10 13 4 ---
**Author:** ![j\_sum1](https://avatars.discourse-cdn.com/v4/letter/j/8baadc/32.png) [@j\_sum1](https://boards.straightdope.com/u/j_sum1)\ **Post date:** [April 26, 2004, 7:43am UTC](https://boards.straightdope.com/t/challenge-24/241726/12 "2004-04-26T07:43:31Z")
(13-10)_2_4 =24 Now try 7, 7, 3, 3 This one is possible, I guarantee it! ---
**Author:** ![Captain\_Carrot](https://avatars.discourse-cdn.com/v4/letter/c/f0a364/32.png) [@Captain\_Carrot](https://boards.straightdope.com/u/Captain_Carrot)\ **Post date:** [April 28, 2004, 12:35am UTC](https://boards.straightdope.com/t/challenge-24/241726/13 "2004-04-28T00:35:08Z")
Took me a while, but (3+3/7)\*7=24. Probably not too hard: 3, 7, 5, 2 ---
**Author:** ![MaxTheVool](https://avatars.discourse-cdn.com/v4/letter/m/9fc29f/32.png) [@MaxTheVool](https://boards.straightdope.com/u/MaxTheVool)\ **Post date:** [April 28, 2004, 1:07am UTC](https://boards.straightdope.com/t/challenge-24/241726/14 "2004-04-28T01:07:18Z")
OK, I decided to ruin everything by writing a computer program to solve problems of this sort… First of all, 21, 6, 8, 2, is in fact unsolvable. The closest one can come is: ((21)-(6))+((8)+(2)) = 25 ((21)/(2))+((6)+(8)) = 49/2 ((21)+(2))+((8)/(6)) = 73/3 ((21)+(2))+((6)/(8)) = 95/4 (21)+((2)/((6)/(8))) = 71/3 ((21)+(6))-((8)/(2)) = 23 As for 3, 3, 7, 7: (7)\*((3)+((3)/(7))) = 24 Oh, and 7,9,11,4.5 has no solution either Anyhow, with the massive power of this computer program, I have come up with the following question: using 1, 2, 3, and 4 as your 4 numbers, what is the smallest integer which can NOT be generated in this method? ---
**Author:** ![Sternvogel](https://avatars.discourse-cdn.com/v4/letter/s/bc79bd/32.png) [@Sternvogel](https://boards.straightdope.com/u/Sternvogel)\ **Post date:** [April 28, 2004, 1:17am UTC](https://boards.straightdope.com/t/challenge-24/241726/15 "2004-04-28T01:17:03Z")
> [@dwalin](#): > > Probably not too hard: 3, 7, 5, 2 (3 \* 5) + 7 + 2 = 24 How about 3, 3, 7, 12 ? ---
**Author:** ![caymus28](https://avatars.discourse-cdn.com/v4/letter/c/7bcc69/32.png) [@caymus28](https://boards.straightdope.com/u/caymus28)\ **Post date:** [April 28, 2004, 1:25am UTC](https://boards.straightdope.com/t/challenge-24/241726/16 "2004-04-28T01:25:18Z")
((3\*3)-7)\*12=24 2,14.4,3,10 ---
**Author:** ![Skeptico](https://avatars.discourse-cdn.com/v4/letter/s/e19b73/32.png) [@Skeptico](https://boards.straightdope.com/u/Skeptico)\ **Post date:** [April 28, 2004, 3:13am UTC](https://boards.straightdope.com/t/challenge-24/241726/17 "2004-04-28T03:13:27Z")
(14.4_10)/(2_3) = 24 This next one is designed for **MaxTheVool** to specifically test his massively-powerful computer program (sic): ```auto 1002 1528 12345 995141083160 ---- , ---- , ----- , ------------ 3001 6779 67899 76867982607 ``` (Thanks, Mathematica 5 🙂 ) ---
**Author:** ![Vaioman](https://avatars.discourse-cdn.com/v4/letter/v/ecccb3/32.png) [@Vaioman](https://boards.straightdope.com/u/Vaioman)\ **Post date:** [April 28, 2004, 4:11am UTC](https://boards.straightdope.com/t/challenge-24/241726/18 "2004-04-28T04:11:49Z")
> [@caymus28](#): > > ((3\*3)-7)\*12=24 > > 2,14.4,3,10 [14.4/(2\*3)] \* 10 = 24 4.8, 2, 8, 1