If the square root symbol denotes positive and negative why would the plus and minus be necessary?
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.
54 can be formed with only two 4’s: 4!/.4 with a bar over .4 (signifying a repeating decimal = 4/9).
The square root of 4 by convention is +2; only in the equation x squared = 4 can it also be negative.
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.
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?
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.
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.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.
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?
I think you misunderstand “ad hominem.”
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.
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.
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.