Wikipedia:Reference desk/Archives/Mathematics/2013 January 21

= January 21 =

Lanchester Square Law
Tend= 100 tanh-1 0.75 Tend= 97.29 -

However, when I input the data into my scientific calculator, it gives 3685.98.

Any help? I'm puzzled. 184.163.189.234 (talk) 00:40, 21 January 2013 (UTC)
 * you typed it in wrong then, compare here this is how to do it nonsense  ferret  02:55, 21 January 2013 (UTC)

3 3's
In a puzzle book, I found a problem which asked to represent all multiples of 3 upto 48, in three 3's or less. For example: 42 = (3! * 3!) + 3!, 21 = (3! * 3) + 3, 30 = 33 - 3 or 33 + 3. The allowed operations are +, -, /[divide], *[multiply], ab[exponentiation] and ![factorial]. I found them all, except the last two that is 45 and 48. Please help. 117.226.244.43 (talk) 10:20, 21 January 2013 (UTC)
 * I don't have an answer for that, but I'll note that they're both quite easy if you also allow double factorial, since 6!! = 48.--80.109.106.49 (talk) 16:44, 21 January 2013 (UTC)
 * I might be confused but 6!! is a hell of alot more than 48, as 6! is 720... 80.254.147.164 (talk) 17:04, 21 January 2013 (UTC)
 * See double factorial.--80.109.106.49 (talk) 17:07, 21 January 2013 (UTC)
 * If you read that link again, you'll see that double factorials are the products of exclusively odd numbers (1 x 3 x 5 x 7 x 9 ....). There ain't no such thing as 6!!, and if there were, it'd be 1 x 3 x 5 = 15.   --   Jack of Oz   [Talk]  22:27, 21 January 2013 (UTC)
 * Jack, you need to keep reading. "Sometimes n!! is defined for non-negative even numbers as well. One choice..." --Modocc (talk) 22:49, 21 January 2013 (UTC)
 * What on earth does "Sometimes n!! is defined for non-negative even numbers as well. One choice is a definition similar to the one for odd values" mean?
 * Is it defined or not? A definition cannot sometimes exist and sometimes not exist.  And if it does exist, why is there more than "one choice"?  Sounds like extremely unrigorous "mathematics" to me.  --   Jack of Oz   [Talk]  18:30, 22 January 2013 (UTC)
 * There are often different definitions of a mathematical term. See for example 0^0 or Prime number. A rigorous mathematician can clearly state their definition when there is doubt. If reliable sources have different definitions or mention that different definitions exist then it isn't Wikipedia's job to claim which definition is "right". PrimeHunter (talk) 02:44, 23 January 2013 (UTC)


 * I think you can't get 45 or 48 this way. Here are solutions for the smaller numbers for completeness.
 * 0 = 3-3;
 * 3 = 3;
 * 6 = 3!; (! added sgb)
 * 9 = 3*3;
 * 12 = 3!+3!;
 * 15 = 3+3!+3!;
 * 18 = 3*3!;
 * 21 = 3+3*3!;
 * 24 = 3!+3*3!;
 * 27 = 3**3;
 * 30 = 3+3**3;
 * 33 = 33;
 * 36 = 3!*3!;
 * 39 = 3+3!*3!;
 * 42 = 3!+3!*3!;
 * &#x2013; b_jonas 21:44, 21 January 2013 (UTC)
 * Here's some solutions using four threes. Maybe you wanted to allow more operators instead?
 * 45 = 3*(3+3!+3!);
 * 48 = 3!*(3!+3!/3);
 * &#x2013; b_jonas 21:58, 21 January 2013 (UTC)


 * Is 33 allowed by the rules? Also if trying to do all numbers...
 * 1	3/3;
 * 2	3!/3;
 * 4	3+3/3;
 * 5	3!-3/3;
 * 7	3!+3/3;

But I have yet to find 8. There are pages similar on the web but they use different operator lists. -- SGBailey (talk) 21:59, 21 January 2013 (UTC)
 * SGBailey: 33 is allowed, as shown by an example of the OP. If you want a solution for 8, look at the source of this message for a spoiler.    However, I think you can't get 10 from three or less threes.  &#x2013; b_jonas 22:06, 21 January 2013 (UTC)
 * Thx -- SGBailey (talk) 10:53, 22 January 2013 (UTC)
 * OP: maybe you want to allow binomial coefficients? I think those would help you get 45 at least.  &#x2013; b_jonas 22:07, 21 January 2013 (UTC)

@jonas: No, you are only allowed 3 threes to use, I too found solutions for 45, 48 with 4 threes. And double factorial is also easy. I wanted to know that within those rules, but I found it isnt, thanks you all. 117.226.243.253 (talk) 14:13, 22 January 2013 (UTC)


 * Here is a solution for 48 without using the double factorial:
 * [[File:3backwards3factorialtimes3equals48.svg]]
 * (That is, $$ 8*3!=48$$.) -- Sławomir Biały (talk) 13:28, 24 January 2013 (UTC)
 * Ouch. &#x2013; b_jonas 20:46, 24 January 2013 (UTC)
 * LOL! Double sharp (talk) 15:14, 28 January 2013 (UTC)