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Topic: 24 I (Read 3080 times) |
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mikedagr8
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are we able to use brackets?
also i have 2 similar problems.
using 1,5,6,7 and using the mathematical symbols +,-,*,/; find a solution to give an answer of 21. (you may also use brackets)
and the second is using the numbers 2,2; find a solution which equals five. (this is very tricky, but doable, i was able to solve once i learnt how to do it in class!)
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towr
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Re: 24 I
« Reply #1 on: Jul 13th, 2007, 3:52am » |
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Yes, bracket are allowed; or you could use prefix or postfix notation.
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mikedagr8
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Re: 24 I
« Reply #2 on: Jul 13th, 2007, 3:56am » |
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thankyou, are you able to make my problems available in the same format as this 24 I?. i like these; these i find are quite annoying, but obvious.
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towr
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Re: 24 I
« Reply #3 on: Jul 15th, 2007, 8:25am » |
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on Jul 13th, 2007, 3:56am, mikedagr8 wrote:| thankyou, are you able to make my problems available in the same format as this 24 I? |
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You mean on the site? I can't. And William (the admin of the site) has been too busy with his studies to even update it in three years.
Do you have any other functions available to make two 2's into 5, because 2+2 isn't five, nor 2*2, nor 2-2, nor 2/2. So having exhaustively tried every option, I'd have to conclude something is missing from the question; be it additional numbers, operators, functions, or an answer.
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mikedagr8
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Re: 24 I
« Reply #4 on: Jul 15th, 2007, 4:56pm » |
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OK fair enough with William being away. I'll fix this up now so it is very understandable unlike before. Problem 1. In the same formats as the other 24 questions are.
Create the number 21 using only these numbers once each: 1, 5, 6, 7. You may use only the following functions: +, -, *, /. This is not a trick question; for example, the answer does not involve a number system other than base 10.
that is the fisrt puzzle.
the second is this.
Create an answer of five, using only the numbers 2,2 once and once only. so 2+2 does not equal five. You may use any functions you wish (anything at all). This is not a trick question; for example, the answer does not involve a number system other than base 10.
that is the second good luck.
(modified, now it is solveable, my apologies, try now, wow that was a major stuff up, didn't edit it, just copied straight put, my apologies again  )
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| « Last Edit: Jul 16th, 2007, 3:13am by mikedagr8 » |
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towr
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Re: 24 I
« Reply #5 on: Jul 16th, 2007, 1:26am » |
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Well, if we take T(n) as the function that gives the nth triangular number, than T(2)+2 = 5. If we take H(n) to be the the function that gives the nth hexagonal number, than H(2)-2=5
I'll see if I can find one with more standard functions; and the first puzzle also still escapes me. (There's always the option of letting the computer do a brute force search; but it'd be nice to find it without computer help)
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mikedagr8
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Re: 24 I
« Reply #6 on: Jul 16th, 2007, 1:44am » |
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That's hilarious, but that isn't even close to my answer, so you better keep going. 
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towr
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Re: 24 I
« Reply #7 on: Jul 16th, 2007, 3:07am » |
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For a moment there I though the first puzzle was impossible, but it turned out I just made a mistake programming (yeah, I gave in on that point).
6/(1-5/7)
(that divide in the subformula of the other divide provided problems)
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| « Last Edit: Jul 16th, 2007, 3:08am by towr » |
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mikedagr8
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Re: 24 I
« Reply #8 on: Jul 16th, 2007, 3:12am » |
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correct, the other question is fixed now.
( i realised that all the other 24's were pretty much teh exact same as this one, so it wasn't to hard to figure them out, i also found the posts finally to confirm my answers.)
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JohanC
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Re: 24 I
« Reply #9 on: Jul 16th, 2007, 4:49am » |
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on Jul 15th, 2007, 4:56pm, mikedagr8 wrote:| Create an answer of five, using only the numbers 2,2 once and once only. so 2+2 does not equal five. You may use any functions you wish (anything at all). This is not a trick question; for example, the answer does not involve a number system other than base 10. |
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What about ceil(sqrt((2*2)!)) ?
on Jul 16th, 2007, 3:07am, towr wrote:| For a moment there I though the first puzzle was impossible, but it turned out I just made a mistake programming (yeah, I gave in on that point). |
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Be very careful with your reputation, costing you so much hard work.
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pex
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Re: 24 I
« Reply #10 on: Jul 16th, 2007, 4:53am » |
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Or 5 = floor(exp(2) - 2), or 5 = ceiling(-2 * tan(2)).
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| « Last Edit: Jul 16th, 2007, 4:55am by pex » |
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mikedagr8
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Re: 24 I
« Reply #11 on: Jul 16th, 2007, 4:53am » |
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ceil(sqrt((2*2)!)) ? Not the answer i am looking for, and the first part, i don't understand the mathematics, so i wont say yes. Anyone else please confirm if it works out, but my answer is simpler (It would be funny if you wrote it in a different way, but there is only one way i know how to solve it.).
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mikedagr8
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Re: 24 I
« Reply #12 on: Jul 16th, 2007, 4:54am » |
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Same again pex, you posted while i was writing back.
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pex
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Re: 24 I
« Reply #13 on: Jul 16th, 2007, 4:57am » |
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on Jul 16th, 2007, 4:53am, mikedagr8 wrote:| ceil(sqrt((2*2)!)) ? ... Anyone else please confirm if it works out... |
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It does. 2*2 = 4, 4! = 24, sqrt(24) = 4.898979..., ceil(4.898979...) = 5.
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mikedagr8
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Re: 24 I
« Reply #14 on: Jul 16th, 2007, 4:59am » |
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NO, then that is not the correct answer, it is exactly 5, not approximate. Believe me, I learnt about how to do it in school last year, then I remembered this problem from a puzzle book, so i was able to figure it out.
(below year 10 mathematics is required, nothing more)
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pex
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Re: 24 I
« Reply #15 on: Jul 16th, 2007, 5:06am » |
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on Jul 16th, 2007, 4:59am, mikedagr8 wrote:NO, then that is not the correct answer, it is exactly 5, not approximate. Believe me, I learnt about how to do it in school last year, then I remembered this problem from a puzzle book, so i was able to figure it out.
(below year 10 mathematics is required, nothing more) |
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How is ceil(4.898979...) not exactly five?
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mikedagr8
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Re: 24 I
« Reply #16 on: Jul 16th, 2007, 5:07am » |
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because it is rounded, the answer i am looking for is 5.0, just plain old 5, as 1+1 is 2, my solution is just 5, not that one, trust me, otherwise as you can see it is too easy. 
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pex
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on Jul 16th, 2007, 5:07am, mikedagr8 wrote:| because it is rounded, the answer i am looking for is 5.0, just plain old 5, as 1+1 is 2, my solution is just 5, not that one, trust me, otherwise as you can see it is too easy. |
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No! ceil(4.898979...) = 5, equals 5, is exactly 5, is nothing more or less than 5. If you do not want such answers, please do not say that we can use any functions we wish.
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mikedagr8
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Re: 24 I
« Reply #18 on: Jul 16th, 2007, 5:19am » |
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O.K. then, if you say you are correct then you are, not this time, try using maths that a 14 year old understands, because there is a way sipler solution than that complex answer (complex to me as i haven't advanced that far yet into mathematics).
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pex
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Re: 24 I
« Reply #19 on: Jul 16th, 2007, 5:24am » |
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on Jul 16th, 2007, 5:19am, mikedagr8 wrote:| O.K. then, if you say you are correct then you are, not this time, try using maths that a 14 year old understands, because there is a way sipler solution than that complex answer (complex to me as i haven't advanced that far yet into mathematics). |
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I'm sorry, I think I lost my temper a bit.
Ceil (or ceiling) and floor functions are something that a 14-year-old can easily understand, though - although they may not know the names: floor means rounding down to the nearest integer, ceil(ing) means rounding up to the nearest integer.
If we cannot use these rounding functions, I do not see how an answer could exist (except for the matchstick one I attached to my previous post). I'll have to think about it.
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mikedagr8
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Re: 24 I
« Reply #20 on: Jul 16th, 2007, 5:27am » |
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O.K., now we are on the same wavelength, I understand that perfectly, but when you arrived at 4.89... I know it theoretically does equal five when it is rounded, BUT, It is not the answer I am looking for, It needs no rounding, or anything like ceil(ing). And the matchstick is not correct for what i am after either, it requires numbers.
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pex
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Re: 24 I
« Reply #21 on: Jul 16th, 2007, 5:34am » |
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on Jul 16th, 2007, 5:27am, mikedagr8 wrote:| O.K., now we are on the same wavelength, I understand that perfectly, but when you arrived at 4.89... I know it theoretically does equal five when it is rounded, BUT, It is not the answer I am looking for, It needs no rounding, or anything like ceil(ing). And the matchstick is not correct for what i am after either, it requires numbers. |
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Fine. Could you also confirm that it's not something silly like "define f(x,y) = x2 + y/2; now observe f(2,2) = 5"?
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pex
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Re: 24 I
« Reply #22 on: Jul 16th, 2007, 6:22am » |
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Maybe it is allowed to use only one 2, mirror it upside down and obtain something that looks like a 5. Or, along the same lines but using two 2s, mirror one of them and place the other in front of it (result: 25) and take the square root.
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Aryabhatta
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Re: 24 I
« Reply #23 on: Jul 16th, 2007, 10:03am » |
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on Jul 16th, 2007, 5:19am, mikedagr8 wrote:| O.K. then, if you say you are correct then you are, not this time, try using maths that a 14 year old understands, because there is a way sipler solution than that complex answer (complex to me as i haven't advanced that far yet into mathematics). |
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Pex's answer is correct. The final answer is exactly 5, no approximations or anything.
Your attitude amazes me Mike. You get angry when someone even makes a mention of your age, and now you want people to post only solutions keeping your age in mind?
Also, pex's solution is perfectly correct given the way the problem was stated. There are an _infinite_ number of correct answers to your problem, so if you want us to find out about the _one_ _you_ came up with, then you will have to give some hints.
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towr
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Re: 24 I
« Reply #24 on: Jul 16th, 2007, 10:13am » |
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He did give some hints, namely that the type of functions and operations involved are ones common enough to be know by 14 year olds. And that no rounding is involved.
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