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animeshsaxena
Posts: 520
Joined: June 19th, 2008, 2:56 pm

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May 13th, 2011, 10:26 pm

QuoteOriginally posted by: outrunOne more:A C-number is a number that can be created from it's own digits with the following rules: * you can use the four operators: + - * /* you can use brackets ( )* you need to use each digit exactly twiceExample:144 = (4-1) * (4-1) 4 * 4For 2 points. How many binary (base 2) C-numbers are there?Example of a binary C-number:3 decimal = 11 binary -> we need to use four 1's. 3 = 1 + 1 + 1/1Couldn't find anything after 2, 3 , 7 (Binary C-numbers).
 
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bwarren
Posts: 128
Joined: February 18th, 2011, 10:44 pm

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May 14th, 2011, 12:05 am

1, 15, and 63 are also binary C-numbers.15 = 1111 = 3 * 5 = (1 + 1 + 1) * (1 + 1 + 1 + 1 + 1)63 = 111111 = 3 * 3 * 7 = (1 + 1 + 1) * (1 + 1 + 1) * (1 + (1 + 1) * (1 + 1 + 1))Not sure what the pattern is...
 
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animeshsaxena
Posts: 520
Joined: June 19th, 2008, 2:56 pm

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May 14th, 2011, 1:12 am

i had thought of all 1's being the pattern but couldn't make 15 and 63...C-numbers...i guess all numbers with all 1's are C-numbers. (2 is an exception)
 
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animeshsaxena
Posts: 520
Joined: June 19th, 2008, 2:56 pm

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May 14th, 2011, 1:17 am

again 31 is a problem....so not a pattern!
 
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wileysw
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Joined: December 9th, 2006, 6:13 pm

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May 14th, 2011, 10:39 pm

outrun, i think T4A & katastrofa both have valid points: i did assume it is simply a square, but the problem would work if it is a rectangle as well - the green circle is just the inscribed circle of the triangle. the same method applies, since the area and the circumference of the triangle are easy to calculate.your new problem seems to be related to the lower bound of integer complexity (is that the "C"?) and i believe the numbers listed here (1,2,3,7,15,63) are the only solutions (checked up to n=10,000. MCarreira would do a much better job:P). unfortunately the apparent bound 3*log3(n) does not seem to do the trick... will update
Last edited by wileysw on May 14th, 2011, 10:00 pm, edited 1 time in total.
 
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Traden4Alpha
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Joined: September 20th, 2002, 8:30 pm

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May 19th, 2011, 11:30 am

You mean perpendicular to the hypotenuse, right?
 
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Traden4Alpha
Posts: 23951
Joined: September 20th, 2002, 8:30 pm

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May 19th, 2011, 2:45 pm

So many puzzles hinge of the exact definition that the literal wording becomes a key input of the solution process. At the same time, real world brainteasers lack explicit/exact definitions such that any example definition of a real-world problem can (and should) be looked at from the standpoint of variants of the problem statement (either relaxing the definition or added sensible constraints) that create a fan of possible solutions, some of which may be better than the solutions derived from the literal reading of the definition.
 
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lindavincent
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Joined: May 24th, 2011, 8:32 am

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May 25th, 2011, 5:22 am

I think I should share here one of the brainteaser which I'd enjoyed most - http://www.iqtestexperts.com/brainteasers/
 
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MCarreira
Posts: 1724
Joined: July 14th, 2002, 3:00 am

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May 26th, 2011, 2:54 am

QuoteOriginally posted by: outrunOne more:A C-number is a number that can be created from it's own digits with the following rules: * you can use the four operators: + - * /* you can use brackets ( )* you need to use each digit exactly twiceExample:144 = (4-1) * (4-1) 4 * 4For 2 points. How many binary (base 2) C-numbers are there?Example of a binary C-number:3 decimal = 11 binary -> we need to use four 1's. 3 = 1 + 1 + 1/1Would 10/(1+1) + 0*1 = 5 be valid ?
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