# Five 4's puzzler **URL:** \ **Category:** The Show\ **Created:** [June 12, 2010, 3:32pm UTC](https://community.cartalk.com/t/five-4s-puzzler/50221 "2010-06-12T15:32:17Z")\ **Posts on this page:** 15\ **Page:** 2
**Author:** ![palebluedot](https://avatars.discourse-cdn.com/v4/letter/p/f17d59/32.png) [@palebluedot](https://community.cartalk.com/u/palebluedot)\ **Post date:** [June 16, 2010, 8:47pm UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/21 "2010-06-16T20:47:18Z")
> **[Square root](https://en.wikipedia.org/wiki/Square_root)** > > In mathematics, a square root of a number a is a number y such that y2 = a; in other words, a number y whose square (the result of multiplying the number by itself, or y⋅y) is a. For example, 4 and −4 are square roots of 16 because 42 = (−4)2 = 16. Every nonnegative real number a has a unique nonnegative square root, called the principal square root, which is denoted by √a, where √ is called the radical sign or radix. For example, the principal square root of 9 is 3, which is denoted by √9 = 3 Ev... ---
**Author:** ![palebluedot](https://avatars.discourse-cdn.com/v4/letter/p/f17d59/32.png) [@palebluedot](https://community.cartalk.com/u/palebluedot)\ **Post date:** [June 16, 2010, 8:56pm UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/22 "2010-06-16T20:56:45Z")
If the square root symbol denotes positive and negative why would the plus and minus be necessary? ---
**Author:** ![ZombieWoof](https://avatars.discourse-cdn.com/v4/letter/z/91b2a8/32.png) [@ZombieWoof](https://community.cartalk.com/u/ZombieWoof)\ **Post date:** [June 17, 2010, 2:52am UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/23 "2010-06-17T02:52:17Z")
If you had read the wiki article you posted a link to you would understand. Of course a math course would help. “A quadratic equation with real or complex coefficients has two solutions, called roots. These two solutions may or may not be distinct, and they may or may not be real.” Let’s Keep It Simple, Simon. Imagine the 4ac - b^2 part under the radical sign evaluates to negative one. Is i positive or negative? Hence the need for the plus or minus. I’m not here to teach you math, just correct your errors. ---
**Author:** ![KevinMagnan](https://avatars.discourse-cdn.com/v4/letter/k/dec6dc/32.png) [@KevinMagnan](https://community.cartalk.com/u/KevinMagnan)\ **Post date:** [June 19, 2010, 3:32pm UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/24 "2010-06-19T15:32:33Z")
54 can be formed with only two 4’s: 4!/.4 with a bar over .4 (signifying a repeating decimal = 4/9). ---
**Author:** ![KevinMagnan](https://avatars.discourse-cdn.com/v4/letter/k/dec6dc/32.png) [@KevinMagnan](https://community.cartalk.com/u/KevinMagnan)\ **Post date:** [June 19, 2010, 3:38pm UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/25 "2010-06-19T15:38:04Z")
The square root of 4 by convention is +2; only in the equation x squared = 4 can it also be negative. ---
**Author:** ![ZombieWoof](https://avatars.discourse-cdn.com/v4/letter/z/91b2a8/32.png) [@ZombieWoof](https://community.cartalk.com/u/ZombieWoof)\ **Post date:** [June 19, 2010, 11:10pm UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/26 "2010-06-19T23:10:28Z")
True, but that wasn’t the Puzzler. 54 can be formed with any number of 4’s greater than 1, and I’m not ruling out the possibility that it could be formed with only one 4. ---
**Author:** ![JoeMario](https://avatars.discourse-cdn.com/v4/letter/j/3bc359/32.png) [@JoeMario](https://community.cartalk.com/u/JoeMario)\ **Post date:** [June 20, 2010, 11:30am UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/27 "2010-06-20T11:30:14Z")
ZombieWolf wrote: > Oh goodness gracious. Your first sentence about the cube (not “cubed”) root was right. Your second sentence is wrong, when you say “the symbol should have a two.” The symbol DOES NOT have a two, and I suspect you are not the official arbiter of mathematical symbols. Your third sentence is also wrong, because a) you don’t understand the radical symbol, and b) you don’t understand the quadratic equation. You misunderstand the part that is pronounced “plus or minus” and means addition or subtraction. This is first semester calculus, at most. It’s probably algebra. Read what article? You are wrong, I am right. Thank you ZombieWolf. How did I, or any of us, ever manage all these years? ---
**Author:** ![KevinMagnan](https://avatars.discourse-cdn.com/v4/letter/k/dec6dc/32.png) [@KevinMagnan](https://community.cartalk.com/u/KevinMagnan)\ **Post date:** [June 21, 2010, 3:35pm UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/28 "2010-06-21T15:35:54Z")
``` With the inclusion of the integer function (and others) new solutions come so readily it seems like cheating. 54 can also be formed with two fours: INT(sinh 4)* SQR 4 or INT(SQR SQR SQR SQR ((4!)!)) + 4! (For those sticklers who insist I must have five 4's to discuss the issue simply add (4 - 4) * 4.) As I understand it the integer function rounds off to the higher absolute value on the negative side: 4! - INT (-SQR SQR SQR SQR ((4!)!)) = 55 with only two fours. Many values can be formed with just one four: INT(SQR SQR 4) = 1 INT(sinh SQR 4) = 3 -INT(-SQR 4!) = 5 ``` I have yet to find a way to form 54 or 55 with just one 4 leaving me with the yucky feeling that I have too much time on my hands. ---
**Author:** ![KevinMagnan](https://avatars.discourse-cdn.com/v4/letter/k/dec6dc/32.png) [@KevinMagnan](https://community.cartalk.com/u/KevinMagnan)\ **Post date:** [June 22, 2010, 12:30am UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/29 "2010-06-22T00:30:34Z")
``` I found it! INT(ln((4!)!)) = 54; just one 4. (To make it relevant to the puzzler simply include + 4 - 4 + 4 - 4.) Also -INT(-ln((4!)!)) = 55; just one 4. I sincerely doubt these are the only solutions. ``` ---
**Author:** ![jt1979](https://sea1.discourse-cdn.com/cartalk/user_avatar/community.cartalk.com/jt1979/32/1863_2.png) [@jt1979](https://community.cartalk.com/u/jt1979)\ **Post date:** [June 22, 2010, 12:51am UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/30 "2010-06-22T00:51:16Z")
You should feel “yucky” about having too much time on your hands! Sheesh! However, the puzzler says you can use math operators, not functions. It seems clear that the intention is to use only SYMBOLS to denote mathematical operations. The “INT” is clearly a function, and I would think that even logarithmic and trigonometric functions would be off limits as well. That being said, it’s interesting that you were able to find a way to do it, even if it doesn’t meet with the letter of the puzzler. ---
**Author:** ![ZombieWoof](https://avatars.discourse-cdn.com/v4/letter/z/91b2a8/32.png) [@ZombieWoof](https://community.cartalk.com/u/ZombieWoof)\ **Post date:** [June 22, 2010, 4:10am UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/31 "2010-06-22T04:10:22Z")
I’m sorry you were peeved. I’m sure you will get along just fine. Thank you for the ad hominem attack. You have a nice day, now, you hear? ---
**Author:** ![jt1979](https://sea1.discourse-cdn.com/cartalk/user_avatar/community.cartalk.com/jt1979/32/1863_2.png) [@jt1979](https://community.cartalk.com/u/jt1979)\ **Post date:** [June 22, 2010, 4:40am UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/32 "2010-06-22T04:40:51Z")
I think you misunderstand “ad hominem.” ---
**Author:** ![KevinMagnan](https://avatars.discourse-cdn.com/v4/letter/k/dec6dc/32.png) [@KevinMagnan](https://community.cartalk.com/u/KevinMagnan)\ **Post date:** [June 22, 2010, 3:51pm UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/33 "2010-06-22T15:51:44Z")
To some mathematicians brackets [] can be used to denote the integer function which are symbols. [SQR SQR 4] = 1. SQR is a function which is allowed; I just don’t have the radical symbol readily available on my keyboard. ---
**Author:** ![GooeyChewie](https://avatars.discourse-cdn.com/v4/letter/g/e47c2d/32.png) [@GooeyChewie](https://community.cartalk.com/u/GooeyChewie)\ **Post date:** [June 23, 2010, 12:00pm UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/34 "2010-06-23T12:00:23Z")
I got a different answer than the Car Talk guys. I got: 4! + 4! + 4/.4 - 4 = 54. 4! = 4 x 3 x 2 x 1 = 24 4/.4 = 10 So, 24 + 24 = 48, 48 + 10 = 58, 58 - 4 = 54. ---
**Author:** ![ZombieWoof](https://avatars.discourse-cdn.com/v4/letter/z/91b2a8/32.png) [@ZombieWoof](https://community.cartalk.com/u/ZombieWoof)\ **Post date:** [June 24, 2010, 5:40am UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/35 "2010-06-24T05:40:47Z")
While I’ve always thought Puzzlers should be solved within the week, I have participated in discussions long past the sell-by date. Your solution is excellent. [Previous page](https://community.cartalk.com/t/five-4s-puzzler/50221.md?page=1)