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Title: Making 32 from Two 2s Post by william wu on Nov 16th, 2002, 6:53pm Create the number 32 using the number "2" only twice. You may use only the following operators: ., +, -, *, /, sqrt() Note 1: What is a "." operator you ask? Prepend a number x with a "." to make .x, such that .(3) --> .3 Also, you can concatenate two numbers x and y with the ".", such that .(5,3) = 5.3 (yes, this is a very strange operator so obviously it's pretty useful toward arriving at a solution ::) ) Note 2: The answer does not necessarily involve a number system other than base 10. Note 3: Writing credits to Anwis Das. // UPDATE 9:00 PM 11/17/2002 Removed the following functions: sin(), cos(), tan(), floor(), ceiling(). |
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Title: Re: Making 32 from Two 2s Post by SWF on Nov 17th, 2002, 12:31pm The "." operator is unnecessary (as is the second 2): _______Spoiler________________ There are many ways to get 32 using these functions. Here are a couple: With two 2's: 32=floor(tan( sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(2))))))))))) +sin(sin(sin(sin(sin(sin(sin(2))))))) )) With only one 2: 32= ceiling(tan(tan(sqrt(sqrt(sqrt(sqrt(sqrt( sin(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt( sin(2)))))))))))))))))) With enough nested square roots and sines inside of tan(tan()), I believe one could get arbitrarily close to 32 using only one 2. ____________________________ |
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Title: Re: Making 32 from Two 2s Post by william wu on Nov 17th, 2002, 7:49pm Ok, I removed a whole bunch of functions from the palette now. I think they were intended to be red herrings, but as you've shown, it didn't work out that way :) |
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Title: Re: Making 32 from Two 2s Post by towr on Nov 18th, 2002, 1:22am hmm.. if you had a two argument root-operator instead of sqrt, you could do root(2, .2) (which is 2^(1/0.2) = 32) Since you only have 2 numbers, and +, -, *, / use two argument you can only use one of those once. I don't think using . more than once on one number makes any sense (what would ..2 be?) So unless it's a trick solution like 31+2/2 (only two 2s) I don't see it whithout at least some of those other operators.. |
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Title: Re: Making 32 from Two 2s Post by william wu on Nov 18th, 2002, 3:38am Yea towr, that was the intended solution. But sqrt() is misleading because it means square root. On paper, Anwis just wrote the radical sign for me, but I never figured to put a .2 into the left-hand side of the radical ... I guess it's cheating. And a two-argument root-operator would probably make the problem too obvious. Scratch this problem. |
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Title: Re: Making 32 from Two 2s Post by towr on Nov 18th, 2002, 8:15am well, you don't necessarily have to specify it's a two-argument root-operator. You could also scan it (or use a graphics program) and show the image. Its a nice problem aside from the problems found.. If you only remove the tan() from the original problem I don't think there are any other solutions either, since tan is the only operator that can make the number sufficiently larger, aside from root. You could even include log and powers i think.. (probably not exp though) |
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Title: Re: Making 32 from Two 2s Post by william wu on Nov 18th, 2002, 12:30pm Hmm ... yeah I thought about that but, I dunno. If I just display the image of a radical, doesn't not having any number in the left-hand side of the radical imply that it must be a square root? |
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Title: Re: Making 32 from Two 2s Post by jeremiahsmith on Nov 18th, 2002, 1:07pm Maybe you could specify that you're allowed to use non-square bases as the radix. |
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Title: Re: Making 32 from Two 2s Post by towr on Nov 18th, 2002, 1:36pm hmm.. I think you may be right about the 'blank' radical having to be the square root.. Mathematical notation allways tends to be unambiguous, which is of course its purpose. So writing everything out on the other hand might help obfuscate the solution sufficiently.. You could perhaps phrase it as "you can use addition, subtraction, multiplication, division, powers, roots, sine, cosine, ceiling (rounding up) and floor (rounding down). Aside from that you can also use the . operator which works in a way that .(3) = .3 and .(5,3) = 5.3" |
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Title: Re: Making 32 from Two 2s Post by Tarazik on Nov 28th, 2002, 7:39pm k, what about if you forget all the extremely complicated math and look at the wording.... Create the number 32 using the number "2" only twice it says nothing about other numbers.... how about 2+12+18? that is techincally only using the number two twice? Or....if you argue that you can't use other numbers, what if you took one number two 2 and then took the second two, flipped it so it was backwards and upside down and looked like a 5, and used it as a exponent? 25=32 just some thoughts.... |
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Title: Re: Making 32 from Two 2s Post by jeremiahsmith on Dec 1st, 2002, 4:38pm on 11/28/02 at 19:39:34, Tarazik wrote:
Doing that would make the riddle so trivial as to be pointless :/ |
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Title: Re: Making 32 from Two 2s Post by towr on Dec 2nd, 2002, 1:22am well, not totally pointless.. If an answer to a riddle is too obvious most people won't think it's the right answer.. |
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Title: Re: Making 32 from Two 2s Post by jeremiahsmith on Dec 2nd, 2002, 10:28am I dunno. Riddles usually involve some mental leap of brilliance, and I dislike puzzles where the mental leap consists of nothing more than "Hey, let's try the obvious answer!" Obvious answers are often bad riddles, in my humble opinion. |
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Title: Re: Making 32 from Two 2s Post by towr on Dec 2nd, 2002, 11:02am I guess that's true often enough.. another way to look at the problem, digital numbering: _ _ _ _though I guess that's without using any of the named operators :p |
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