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Topic: 181 (Read 1057 times) |
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ThudnBlunder
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I'm not sure if this is Easy to figure out:
Express 181 using the integers 2, 5, and 7 once only (together with the usual operators such as addition, division, power, etc).
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Barukh
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Re: 181
« Reply #1 on: Aug 24th, 2006, 11:27pm » |
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What's "etc" here? Is log allowed? Square root? Decimal point? ...
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ThudnBlunder
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Re: 181
« Reply #2 on: Aug 25th, 2006, 4:30am » |
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on Aug 24th, 2006, 11:27pm, Barukh wrote:| What's "etc" here? Is log allowed? Square root? Decimal point? ... |
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I thought 'power' included square root.
'Decimal point' is not an operator.
To be specific, let the operators be addition, subtraction, multiplication, division, and power.
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Sameer
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Re: 181
« Reply #3 on: Aug 25th, 2006, 10:31am » |
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Also one more clarification hoping that it is not one of those clever word plays from T&B  . You are allowed to use 2,5,7 once only.. how about other integers?
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| « Last Edit: Aug 25th, 2006, 10:31am by Sameer » |
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ThudnBlunder
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Re: 181
« Reply #4 on: Aug 25th, 2006, 11:51am » |
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on Aug 25th, 2006, 10:31am, Sameer wrote:| Also one more clarification hoping that it is not one of those clever word plays from T&B . You are allowed to use 2,5,7 once only.. how about other integers? |
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What do you take me for, Sameer? 
No, this is not a wordplay.
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Icarus
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Re: 181
« Reply #5 on: Aug 25th, 2006, 7:02pm » |
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Who can trust a face like that?
Yet another clarification... Does taking the square root require your sole use of "2"?
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ThudnBlunder
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Re: 181
« Reply #6 on: Aug 25th, 2006, 8:06pm » |
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on Aug 25th, 2006, 7:02pm, Icarus wrote:| Yet another clarification... Does taking the square root require your sole use of "2"? |
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No, 'sqrt' is OK.
Correction: let the operators be addition, subtraction, multiplication, division, power, and factorial.
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Sameer
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Re: 181
« Reply #7 on: Aug 25th, 2006, 10:27pm » |
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This was really bothering my sleep... so I did some searching and stumbled into this
http://mathworld.wolfram.com/RamanujansSquareEquation.html
From this the answer was easy to deduce.. especially after T&B allowed us the use of factorials and sqrts!! 
P.S. I couldn't hide the URL 
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| « Last Edit: Aug 25th, 2006, 10:28pm by Sameer » |
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"Obvious" is the most dangerous word in mathematics.
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Proof is an idol before which the mathematician tortures himself.
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Oyibo
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Re: 181
« Reply #8 on: Aug 26th, 2006, 1:00am » |
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on Aug 25th, 2006, 10:27pm, Sameer wrote:| From this the answer was easy to deduce.. especially after T&B allowed us the use of factorials and sqrts!! |
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But that requires double factorials, isn't it? It was not stated whether these were allowed...
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ThudnBlunder
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Re: 181
« Reply #9 on: Aug 26th, 2006, 1:41am » |
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on Aug 26th, 2006, 1:00am, Oyibo wrote:
But that requires double factorials, isn't it? It was not stated whether these were allowed...
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No, it doesn't.
Well done, Sameer. You out-Googled everybody else.
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| « Last Edit: Aug 26th, 2006, 1:41am by ThudnBlunder » |
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Icarus
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Re: 181
« Reply #10 on: Aug 26th, 2006, 10:09am » |
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on Aug 25th, 2006, 10:27pm, Sameer wrote:| P.S. I couldn't hide the URL |
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Try this:
Code:| [url=<your url here>]<your descriptive text here>[/url] |
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Deedlit
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Re: 181
« Reply #11 on: Aug 26th, 2006, 10:27am » |
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But how do you get 215 using just 2 and 5?
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ThudnBlunder
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Re: 181
« Reply #12 on: Aug 26th, 2006, 11:00am » |
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on Aug 26th, 2006, 10:27am, Deedlit wrote:| But how do you get 215 using just 2 and 5? |
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...and 'sqrt' and 'factorial'. 
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| « Last Edit: Aug 26th, 2006, 11:26am by ThudnBlunder » |
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Sameer
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Re: 181
« Reply #13 on: Aug 26th, 2006, 11:15am » |
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on Aug 26th, 2006, 1:41am, THUDandBLUNDER wrote:
No, it doesn't.
Well done, Sameer. You out-Googled everybody else. |
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I wish I googled!!! I started out with thinking this was some base trick. Trying to put 181 in different bases. Then approached it with something to do with primes. So I went to wolfram site and started searching on prime multiplication, prime factorization and what not and after going through so many links stumbled on this one and I was positively surprised!! 
Hee hee and even with the equation out I see there is still some confusion as to how to get to 15!!
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"Obvious" is the most dangerous word in mathematics.
--Bell, Eric Temple
Proof is an idol before which the mathematician tortures himself.
Sir Arthur Eddington, quoted in Bridges to Infinity
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ThudnBlunder
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Re: 181
« Reply #14 on: Aug 26th, 2006, 11:39am » |
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Hmm...seems like I will have to find one that is not at Mathworld.
Ok, same problem but with 1, 2, 3 - and 19 as the target number. 
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| « Last Edit: Aug 26th, 2006, 11:41am by ThudnBlunder » |
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Eigenray
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Re: 181
« Reply #15 on: Aug 26th, 2006, 8:34pm » |
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sqrt(3!!/2 + 1)
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ThudnBlunder
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Re: 181
« Reply #16 on: Aug 27th, 2006, 5:48am » |
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on Aug 26th, 2006, 8:34pm, Eigenray wrote:
Correct, except for a pair of missing brackets, and a consequence of the identity
n!/(n - 4)! = (n2 - 3n + 1)2 - 1.
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| « Last Edit: Aug 27th, 2006, 5:50am by ThudnBlunder » |
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Death
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Re: 181
« Reply #17 on: Aug 29th, 2006, 5:04am » |
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errrr...... i'm not sure if i'm missing something here, but couldn't you just write 19 as 2(32)+1? 
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towr
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Re: 181
« Reply #18 on: Aug 29th, 2006, 5:17am » |
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on Aug 29th, 2006, 5:04am, Death wrote:| errrr...... i'm not sure if i'm missing something here, but couldn't you just write 19 as 2(32)+1? |
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Not without using one more 2 than you're allowed.
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Sjoerd Job Postmus
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Re: 181
« Reply #19 on: Aug 29th, 2006, 8:53am » |
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on Aug 29th, 2006, 5:17am, towr wrote:
Not without using one more 2 than you're allowed. |
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Well, maybe
2*sqr(3)+1
would suffice then. After all, sqr(3) = 3^2... but I didn't use a 2 in sqr(3)... 
I can do it if I may define a function too
soln(a,b,c) = 19*(a/b)*(b/c)*(c/a)
19 = soln(1,2,3).
And, a bit less cheating, I guess...
(never mind, I don't know)
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