# 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:** 20\ **Page:** 1
**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 12, 2010, 3:32pm UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/1 "2010-06-12T15:32:17Z")
Oops, first time posting and I accidentally put this in “repairs and maintenance” the first time! I thought this would take longer to figure out. Did anyone else come up with another way to do it? I got: ((4^4)/4)-(4/.4) = 54 ---
**Author:** ![meroche](https://avatars.discourse-cdn.com/v4/letter/m/bc8723/32.png) [@meroche](https://community.cartalk.com/u/meroche)\ **Post date:** [June 13, 2010, 11:28am UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/2 "2010-06-13T11:28:36Z")
yeah I got that too. Four 4s is even easier. 44+4/.4=54 This works too and is the second grade answer: 44+4+4+sqrt(4)=54 ---
**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 13, 2010, 3:55pm UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/3 "2010-06-13T15:55:59Z")
It doesn’t surprise me that I would completely overlook a simpler answer! Although, I suppose a person could make the argument that the square root of 4 is both 2 and -2, so that equation is necessarily correct. ---
**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 13, 2010, 3:58pm UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/4 "2010-06-13T15:58:02Z")
Oops. That should say, “ISN’T necessarily correct.” ---
**Author:** ![ZombieWoof](https://avatars.discourse-cdn.com/v4/letter/z/91b2a8/32.png) [@ZombieWoof](https://community.cartalk.com/u/ZombieWoof)\ **Post date:** [June 14, 2010, 1:37am UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/5 "2010-06-14T01:37:23Z")
“Four 4s is even easier” is just making a new puzzle and doesn’t count as an answer. Your simple answer was good. I agree with jt1979 that this one was pretty easy. I arrived at his answer while waiting for this page to load. There are many other solutions, using trigonometric functions, factorials, percents, floors, ceilings, mods, etc. Try wiki’ing “mathematical functions” or “mathematical notation”. I also agree that sqrt disqualifies the simpler solution. Need to put an absolute value sign around that. ---
**Author:** ![palebluedot](https://avatars.discourse-cdn.com/v4/letter/p/f17d59/32.png) [@palebluedot](https://community.cartalk.com/u/palebluedot)\ **Post date:** [June 14, 2010, 2:14am UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/6 "2010-06-14T02:14:37Z")
[http://mathworld.wolfram.com/SquareRoot.html](http://mathworld.wolfram.com/SquareRoot.html) You actually don’t need the absolute value, but the square root should not be allowed because it uses 4^1/2. ---
**Author:** ![ZombieWoof](https://avatars.discourse-cdn.com/v4/letter/z/91b2a8/32.png) [@ZombieWoof](https://community.cartalk.com/u/ZombieWoof)\ **Post date:** [June 14, 2010, 11:33am UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/7 "2010-06-14T11:33:05Z")
Well, no, it doesn’t. Square root uses the square root sign (and this was specifically spelled out on the show… learn to listen, listen to learn) so you are wrong, and you DO need to indicate the absolute value. You are wrong. ---
**Author:** ![palebluedot](https://avatars.discourse-cdn.com/v4/letter/p/f17d59/32.png) [@palebluedot](https://community.cartalk.com/u/palebluedot)\ **Post date:** [June 14, 2010, 12:39pm UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/8 "2010-06-14T12:39:38Z")
They also said in the show that cubed could not be used because it used a 3. The symbol should have a two, but it is understood. Also, the square root symbol means the positive root. If it didn’t then there would be no point in indicating it on the quadratic formula. There would just be a + and no -. Read the article. So you’re wrong. ---
**Author:** ![ZombieWoof](https://avatars.discourse-cdn.com/v4/letter/z/91b2a8/32.png) [@ZombieWoof](https://community.cartalk.com/u/ZombieWoof)\ **Post date:** [June 15, 2010, 6:43am UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/9 "2010-06-15T06:43:10Z")
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. > **[Quadratic equation](https://en.wikipedia.org/wiki/Quadratic_equation)** > > In algebra, a quadratic equation (from the Latin quadratus for "square") is any equation having the form where x represents an unknown, and a, b, and c represent known numbers such that a is not equal to 0. If a = 0, then the equation is linear, not quadratic. The numbers a, b, and c are the coefficients of the equation, and may be distinguished by calling them, respectively, the quadratic coefficient, the linear coefficient and the constant or free term. Because the quadratic equation involves o... ---
**Author:** ![DanAxtell](https://avatars.discourse-cdn.com/v4/letter/d/58956e/32.png) [@DanAxtell](https://community.cartalk.com/u/DanAxtell)\ **Post date:** [June 15, 2010, 1:07pm UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/10 "2010-06-15T13:07:12Z")
Only two 4s are needed by using a viniculum. It’s a variation on the Nov. 7, 2009 “55” puzzler solution discussed here: [http://community.cartalk.com/posts/list/2131829.page](http://community.cartalk.com/posts/list/2131829.page). ---
**Author:** ![palebluedot](https://avatars.discourse-cdn.com/v4/letter/p/f17d59/32.png) [@palebluedot](https://community.cartalk.com/u/palebluedot)\ **Post date:** [June 15, 2010, 1:19pm UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/11 "2010-06-15T13:19:26Z")
I understand the symbol means plus or minus. Why does the radical not have an absolute value sign? Read the article that I posted. The square root symbol means the principal square root (the positive one). ---
**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 15, 2010, 1:32pm UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/12 "2010-06-15T13:32:28Z")
That’s a “vinculum,” not “viniculum.” And, while it’s interesting, two 4’s, three 4’s, and four 4’s are all irrelevant to the topic, since the puzzler requires five 4’s. Interesting use of notation that nobody would probably think of though. How about: 4_4_4_4_4 = 54 (in base 204) ---
**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 15, 2010, 3:37pm UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/13 "2010-06-15T15:37:46Z")
As I pointed out earlier it doesn’t surprise me that I would overlook a simpler answer and try to overthink this. I just realized that, in my original answer, instead of writing ((4^4)/4), you could write (4_4_4) and it would yield the same result, be simpler, and still use three 4’s. I must have secretly wanted it to be more difficult because I was expecting it to be. ---
**Author:** ![texases](https://sea1.discourse-cdn.com/cartalk/user_avatar/community.cartalk.com/texases/32/862_2.png) [@texases](https://community.cartalk.com/u/texases)\ **Post date:** [June 15, 2010, 5:12pm UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/14 "2010-06-15T17:12:19Z")
Here’s the text version of part of the Puzzler: “You can use any of the math operators you want: addition, subtraction, decimals, fractions, square roots, factorial, any of that stuff. You can?t use cube roots because you?d be using the number 3. You can only use the number 4.” So T&R are allowing the square root, because it requires no use of the number ‘2’, while a cube root requires use of the number ‘3’. ---
**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 15, 2010, 5:25pm UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/15 "2010-06-15T17:25:34Z")
I read the article. It says, “In general usage… the square root sign is generally taken to mean the principal square root.” That’s a far cry from meaning that the square sign always means the positive, and only the positive, square root. ---
**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 15, 2010, 5:34pm UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/16 "2010-06-15T17:34:37Z")
My mistake, it did not say “square root sign,” merely “the square root.” I guess I “generally” take the square root sign to mean the square root (not necessarily the principle s.r.), and since there are two, I would think it could conceivably mean both. Seems to me that if a middle school math test asked you to find the square root of 4, you might receive only half credit if you didn’t put both 2 and -2. ---
**Author:** ![DanAxtell](https://avatars.discourse-cdn.com/v4/letter/d/58956e/32.png) [@DanAxtell](https://community.cartalk.com/u/DanAxtell)\ **Post date:** [June 15, 2010, 7:04pm UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/17 "2010-06-15T19:04:34Z")
Vin-cu-lum. Thank you. I’ve been spelling it wrong since I learned the word 7 months ago. And I’ve been singing about it to the tune of “Funiculi, Funicula” with the extraneous syllable. No wonder I’ve gotten strange looks. If I must use all five 4s, then I’ll send in (4! / .4 vinculum) + (4 \* (4 - 4)). I like your base 204 solution, but I’m afraid you’ll find that Earth-dwelling humans have an inexplicable fondness of base ten and will vigorously defend its imagined primacy. As an example, I’ve been alerting people born in 1953 that 2010 is a special year because it’s their age in base three. Typically, they respond “What’s base three?” and “Why do I care?” It’s times like that when I most sorely miss my home planet. ---
**Author:** ![ZombieWoof](https://avatars.discourse-cdn.com/v4/letter/z/91b2a8/32.png) [@ZombieWoof](https://community.cartalk.com/u/ZombieWoof)\ **Post date:** [June 16, 2010, 6:43am UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/18 "2010-06-16T06:43:22Z")
You could have made it much simpler by simply leaving out all of the parentheses. 4^4/4-4/.4=54 Order of precedence tells you how to evaluate the equation. ---
**Author:** ![ZombieWoof](https://avatars.discourse-cdn.com/v4/letter/z/91b2a8/32.png) [@ZombieWoof](https://community.cartalk.com/u/ZombieWoof)\ **Post date:** [June 16, 2010, 6:47am UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/19 "2010-06-16T06:47:58Z")
Did you notice the word “generally” in the article you quoted, which was in fact an article about a piece of software, and and not about mathematics? Still wrong. To answer your apparent, but poorly phrased question, the radical in the quadratic equation doesn’t have an absolute value sign around it because of the PLUS OR MINUS part. Jeepers. ---
**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 16, 2010, 1:14pm UTC](https://community.cartalk.com/t/five-4s-puzzler/50221/20 "2010-06-16T13:14:12Z")
I guess that’s technically correct, and it’s simpler in that it saves a few characters in the equation. I guess I would argue that, in its own way, it’s simpler to put parentheses around things to avoid any confusion as to what operations go first or together. It saves someone from trying to decipher it by having to think about the order of operations. I think it looks a little jumbled and confusing without the parentheses. I do a lot of formulas in Excel, and am in the habit of always grouping things with parentheses - I think it greatly lessons the chance of making a mistake somewhere along the way. [Next page](https://community.cartalk.com/t/five-4s-puzzler/50221.md?page=2)