# Math Game: Combining 4 Fours... **URL:** \ **Category:** Factual Questions\ **Created:** [February 5, 2003, 3:37am UTC](https://boards.straightdope.com/t/math-game-combining-4-fours/152870 "2003-02-05T03:37:27Z")\ **Posts on this page:** 20\ **Page:** 3
**Author:** ![Q.E.D](https://avatars.discourse-cdn.com/v4/letter/q/51bf81/32.png) [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)\ **Post date:** [February 5, 2003, 6:24am UTC](https://boards.straightdope.com/t/math-game-combining-4-fours/152870/41 "2003-02-05T06:24:58Z")
19 = 4!-4-(4/4) ---
**Author:** ![Sunspace](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/sunspace/32/1250_2.png) [@Sunspace](https://boards.straightdope.com/u/Sunspace)\ **Post date:** [February 5, 2003, 6:26am UTC](https://boards.straightdope.com/t/math-game-combining-4-fours/152870/42 "2003-02-05T06:26:58Z")
**The Weak Force** , dare I ask what “chained arrows” are? ---
**Author:** ![The\_Weak\_Force](https://avatars.discourse-cdn.com/v4/letter/t/9dc877/32.png) [@The\_Weak\_Force](https://boards.straightdope.com/u/The_Weak_Force)\ **Post date:** [February 5, 2003, 6:54am UTC](https://boards.straightdope.com/t/math-game-combining-4-fours/152870/43 "2003-02-05T06:54:23Z")
Paraphrased from _The Book of Numbers_, by Conway and Guy: a -\> 1 -\> b is a^b. a -\> n -\> b is a -\> (n - 1) -\> (a -\> (n - 1) -\> … (a -\> (n - 1) -\> a )…), where there are b a -\> (n - 1)'s. a -\> … -\> x -\> y -\> (z + 1) is… a -\> … -\> x if y = 1; a -\> … -\> x -\> (a -\> … -\> x -\> (y - 1) -\> (z + 1)) -\> z if y \> 1. Also, a -\> … -\> b -\> 1 is a -\> … -\> b. I hope I got that right… ---
**Author:** ![Urban\_Ranger](https://avatars.discourse-cdn.com/v4/letter/u/e9c0ed/32.png) [@Urban\_Ranger](https://boards.straightdope.com/u/Urban_Ranger)\ **Post date:** [February 5, 2003, 7:01am UTC](https://boards.straightdope.com/t/math-game-combining-4-fours/152870/44 "2003-02-05T07:01:37Z")
> [@](#): > > \*Originally posted by Sunspace \* > MathCad? Hmm. Seeing the exact value of 4[sup]256[/sup] would be interesting for a start. Less than two hundred digits. Are there any indefinite-precision calculators on the web? IIRC, there’s one in Unix. ---
**Author:** ![Urban\_Ranger](https://avatars.discourse-cdn.com/v4/letter/u/e9c0ed/32.png) [@Urban\_Ranger](https://boards.straightdope.com/u/Urban_Ranger)\ **Post date:** [February 5, 2003, 7:04am UTC](https://boards.straightdope.com/t/math-game-combining-4-fours/152870/45 "2003-02-05T07:04:40Z")
> [@](#): > > \*Originally posted by The Weak Force \* > 18 = 44/[symbol]Ö[/symbol]4 - 4 What does the strange looking operator do? I don’t think you are allowed to concatenate the digits, either. ---
**Author:** ![The\_Weak\_Force](https://avatars.discourse-cdn.com/v4/letter/t/9dc877/32.png) [@The\_Weak\_Force](https://boards.straightdope.com/u/The_Weak_Force)\ **Post date:** [February 5, 2003, 7:09am UTC](https://boards.straightdope.com/t/math-game-combining-4-fours/152870/46 "2003-02-05T07:09:27Z")
[symbol]Ö[/symbol] is the radical sign, i.e., square root. ---
**Author:** ![Sunspace](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/sunspace/32/1250_2.png) [@Sunspace](https://boards.straightdope.com/u/Sunspace)\ **Post date:** [February 5, 2003, 7:11am UTC](https://boards.straightdope.com/t/math-game-combining-4-fours/152870/47 "2003-02-05T07:11:59Z")
Whoa. I’m confused, **The Weak Force**. There seem to be several different ways of expanding these expressions. **a -\> 1 -\> b** = **a[sup]b[/sup]** = **a \* a \* a … \* a \* a** (for **b** multiplications of **a** ). What would **a -\> 2 -\> b** be? ---
**Author:** ![Achernar](https://avatars.discourse-cdn.com/v4/letter/a/e274bd/32.png) [@Achernar](https://boards.straightdope.com/u/Achernar)\ **Post date:** [February 5, 2003, 7:12am UTC](https://boards.straightdope.com/t/math-game-combining-4-fours/152870/48 "2003-02-05T07:12:49Z")
> [@](#): > > \*Originally posted by Sunspace \* > MathCad? Hmm. Seeing the exact value of 4[sup]256[/sup] would be interesting for a start. Less than two hundred digits. Are there any indefinite-precision calculators on the web? My TI-89 will do it. 😃 Takes less than a second, but that’s no surprise. What is suprising is that I don’t feel like copying down all 155 digits. This time. 😉 ---
**Author:** ![Sunspace](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/sunspace/32/1250_2.png) [@Sunspace](https://boards.straightdope.com/u/Sunspace)\ **Post date:** [February 5, 2003, 7:17am UTC](https://boards.straightdope.com/t/math-game-combining-4-fours/152870/49 "2003-02-05T07:17:35Z")
**Urban Ranger** , does your machine have the Symbol font? Mine doesn’t, and I’m seeing the alleged square-root sign as a capital O with umlaut. ---
**Author:** ![RM\_Mentock](https://avatars.discourse-cdn.com/v4/letter/r/e274bd/32.png) [@RM\_Mentock](https://boards.straightdope.com/u/RM_Mentock)\ **Post date:** [February 5, 2003, 7:22am UTC](https://boards.straightdope.com/t/math-game-combining-4-fours/152870/50 "2003-02-05T07:22:57Z")
4^256 = 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096 ---
**Author:** ![Urban\_Ranger](https://avatars.discourse-cdn.com/v4/letter/u/e9c0ed/32.png) [@Urban\_Ranger](https://boards.straightdope.com/u/Urban_Ranger)\ **Post date:** [February 5, 2003, 7:39am UTC](https://boards.straightdope.com/t/math-game-combining-4-fours/152870/51 "2003-02-05T07:39:51Z")
> [@](#): > > \*Originally posted by The Weak Force \* > [symbol]Ö[/symbol] is the radical sign, i.e., square root. Oh, okay, it just doesn’t show up that way on my browser. Thanks. ---
**Author:** ![Urban\_Ranger](https://avatars.discourse-cdn.com/v4/letter/u/e9c0ed/32.png) [@Urban\_Ranger](https://boards.straightdope.com/u/Urban_Ranger)\ **Post date:** [February 5, 2003, 7:41am UTC](https://boards.straightdope.com/t/math-game-combining-4-fours/152870/52 "2003-02-05T07:41:39Z")
> [@](#): > > \*Originally posted by Sunspace \* > **Urban Ranger** , does your machine have the Symbol font? Mine doesn’t, and I’m seeing the alleged square-root sign as a capital O with umlaut. Yes, that’s exactly what I am seeing, even though I have the Symbols typeface. I reckon only IE would render it correctly, while I am using Mozilla. ---
**Author:** ![Achernar](https://avatars.discourse-cdn.com/v4/letter/a/e274bd/32.png) [@Achernar](https://boards.straightdope.com/u/Achernar)\ **Post date:** [February 5, 2003, 7:47am UTC](https://boards.straightdope.com/t/math-game-combining-4-fours/152870/53 "2003-02-05T07:47:38Z")
About This Message Board thread: [Symbol font does not work in Netscape](http://boards.straightdope.com/sdmb/showthread.php?s=&threadid=120922) ---
**Author:** ![MonkeyMensch](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@MonkeyMensch](https://boards.straightdope.com/u/MonkeyMensch)\ **Post date:** [February 5, 2003, 9:26am UTC](https://boards.straightdope.com/t/math-game-combining-4-fours/152870/54 "2003-02-05T09:26:32Z")
> [@](#): > > \*Originally posted by RM Mentock \* > \*\*How do you define 4 without 1, 2, and 3? \*\* Well put, RM, but now you’re wallowing in the quicksand of formality… ---
**Author:** ![RM\_Mentock](https://avatars.discourse-cdn.com/v4/letter/r/e274bd/32.png) [@RM\_Mentock](https://boards.straightdope.com/u/RM_Mentock)\ **Post date:** [February 5, 2003, 2:00pm UTC](https://boards.straightdope.com/t/math-game-combining-4-fours/152870/55 "2003-02-05T14:00:42Z")
Gyan9 grabbed me and dragged me in. Sorry we got mud on y’all. ---
**Author:** ![Sunspace](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/sunspace/32/1250_2.png) [@Sunspace](https://boards.straightdope.com/u/Sunspace)\ **Post date:** [February 5, 2003, 3:07pm UTC](https://boards.straightdope.com/t/math-game-combining-4-fours/152870/56 "2003-02-05T15:07:28Z")
Interesting. I just opened this thread under IE5.0, and none of the multiple exponents are displayed correctly.4[sup]4[sup]4[/sup][/sup] looks like 4[sup]44[/sup]. However, it _does_ show the square-root sign. ---
**Author:** ![Sunspace](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/sunspace/32/1250_2.png) [@Sunspace](https://boards.straightdope.com/u/Sunspace)\ **Post date:** [February 5, 2003, 3:13pm UTC](https://boards.straightdope.com/t/math-game-combining-4-fours/152870/57 "2003-02-05T15:13:26Z")
…and a Google search yielded this page: [http://www.wschnei.de/number-theory/large-numbers.html](http://www.wschnei.de/number-theory/large-numbers.html) Looks like tetration is just a minor bump in the foothills of Large Numbers… ---
**Author:** ![Xerxes](https://avatars.discourse-cdn.com/v4/letter/x/d2c977/32.png) [@Xerxes](https://boards.straightdope.com/u/Xerxes)\ **Post date:** [February 5, 2003, 3:53pm UTC](https://boards.straightdope.com/t/math-game-combining-4-fours/152870/58 "2003-02-05T15:53:18Z")
20 = 4 x (4 + 4/4) 21 = 4! - (4 - 4/4) 22 = 4! - (4 + 4)/4 23 … already done 24 = (4 x 4) + 4 + 4 ---
**Author:** ![Q.E.D](https://avatars.discourse-cdn.com/v4/letter/q/51bf81/32.png) [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)\ **Post date:** [February 5, 2003, 4:17pm UTC](https://boards.straightdope.com/t/math-game-combining-4-fours/152870/59 "2003-02-05T16:17:15Z")
My software won’t let me do 4[sup]4[sup]4[sup]4[/sup][/sup][/sup]. Just as well, it’s probably a scary-big number. :eek: ---
**Author:** ![Q.E.D](https://avatars.discourse-cdn.com/v4/letter/q/51bf81/32.png) [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)\ **Post date:** [February 5, 2003, 4:26pm UTC](https://boards.straightdope.com/t/math-game-combining-4-fours/152870/60 "2003-02-05T16:26:29Z")
Whatever it is, it’s bigger than 268435448 digits! [Previous page](https://boards.straightdope.com/t/math-game-combining-4-fours/152870.md?page=2) [Next page](https://boards.straightdope.com/t/math-game-combining-4-fours/152870.md?page=4)