Math riddle, help please
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thread starter Wasbeer Aug 30 2010
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| Hey, so for school my teacher's given out a math riddle and whoeever solves it and explains why, gets bonus points (0.5) on the upcoming test.... So can you guys help me explain why this riddle's answer is always 1? Take any uneven number, square it (times itself), subtract 1. Any number u've picked should be dividable by 8. HOW COME? My head is aching... |
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xman403 08/30/10
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| This doesnt make any sense an uneven number isnt divisible by an even number |
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ExposedWires
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| [quote] xman403 : This doesnt make any sense an uneven number isnt divisible by an even number [/quote] When he says square it he means multiply it by itself. eg) 5 squared = 5 x 5 which equals 25 OP: Sorry I can't really help you :P I'll think about it some more and post if I figure it out |
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astinus
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| Lets say the number you picked is K+1, such as K is an even number. 1) By definition K is divisible by 2, lets say 2*n = k. N being any real number 2) (K+1)^2 = k^2 + 2k+1 3) k^2 + 2k + 1 -1 = k^2+2k 4) 2*n*2n + 4n. Substitution from step 1 5) 4(n^2+n) = 4n (n+1). 6) Case, n is even. 4*n will be a multiple of 8 Case, n is odd (n+1) will be even so with 4*n, a multiple of 8 [QED] Edit. Initial proof is wrong |
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maniak4lyf 08/30/10
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| It's 3. 3^2 = 9 - 1 = 8/8 = 1 |
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Piyohonke 08/30/10
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| [quote] astinus : Lets say the number you picked is K+1, such as K is an even number. 1) By definition K is divisible by 2, lets say 2*n = k. N being any real number 2) (K+1)^2 = k^2 + 2k+1 3) k^2 + 2k+1 -1 = k^2+2k 4) 2*n*2n + 4n. From 1) 5) 4(2n) = 8n therefore by simple math, it's divisible by 8. [QED] [/quote] I think I fell in love with you. |
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bombinator
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| astinus ooo i like your post way better, nice induction |
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krftw 08/30/10
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| astinus This guy is a genius. |
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tctanalot 08/30/10
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GizzyJones 08/30/10
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| [quote] astinus : Lets say the number you picked is K+1, such as K is an even number. 1) By definition K is divisible by 2, lets say 2*n = k. N being any real number 2) (K+1)^2 = k^2 + 2k+1 3) k^2 + 2k + 1 -1 = k^2+2k 4) 2*n*2n + 4n. Substitution from step 1 5) 4(2n) = 8n therefore by simple math, it's divisible by 8. [QED] Edit. What the end result show is that whatever you picked, you can find a number n such that 8 * n will equal to it. I don't know any more way to explain [/quote] We got a genius up in this thread, or just one in high school math >.> |
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dumbfugi3 08/30/10
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 | [quote] astinus : Lets say the number you picked is K+1, such as K is an even number. 1) By definition K is divisible by 2, lets say 2*n = k. N being any real number 2) (K+1)^2 = k^2 + 2k+1 3) k^2 + 2k + 1 -1 = k^2+2k 4) 2*n*2n + 4n. Substitution from step 1 5) 4(2n) = 8n therefore by simple math, it's divisible by 8. [QED] Edit. What the end result show is that whatever you picked, you can find a number n such that 8 * n will equal to it. I don't know any more way to explain [/quote] How does 2n*2n + 4n go to 4(2n)?... Shouldn't it be 4n^2+4n or 4n(n+1)?... |
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astinus 08/30/10
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| [quote] dumbfugi3 : How does 2n*2n + 4n go to 4(2n)?... Shouldn't it be 4n^2+4n or 4n(n+1)?... [/quote] Thank you I just noticed that error as well I just corrected that with cases |
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dumbfugi3 08/30/10
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| [quote] astinus : Thank you I just noticed that error as well I just corrected that with cases [/quote] You're welcome. It makes sense now. |
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ranger2962
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JtotheEsus 08/30/10
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| Branching off @astinus, imagine K representing an even number. Therefore, the equation would be represented by (K+1)^2 - 1, would be divisible by 8. (Odd number squared, subtract one, divisible by 8) FOIL out the equation to get K^2 + 2K + 1 - 1, simplified to K^2 + 2K, then again to K(K + 2), still divisible by 8. But instead of divisible by 8, imagine it being divisible by 2, three times. 2^3=8 If K represents an even number, 2 would be the first number to fit, the lowest non-negative value. So it would be 2(2 + 2), divisible by 2^3 Cancel out the first 2, you get (2+2) divisible by 2^2, or 4. 4 is always divisible by 4. So, any even number fits into the previously stated equation. |
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