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March 15th, 2010, 08:10 AM  #1 
Newbie Joined: Mar 2010 Posts: 4 Thanks: 0  8th grade proble, challenging???
Problem 1 On each face of a cube a certain natural number was written, and at each vertex a number equal to the product of the numbers on the three faces adjacent to that vertex was placed. If the sum of the numbers on the vertexes is 70 then what is the sum of the numbers on all the faces of the cube? a, 12 b, 35 c, 14 d, 10 e, cannot be determined Problem 2 Pages problem? math grade7 Peter put magazines on a bookshelf. They have either 48 or 52 pages. which of the following number cannot be the total pages of all the magazines on the bookshelf? a, 500 b, 524 c, 568 d, 588 e, 620 
March 15th, 2010, 09:34 AM  #2  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: 8th grade proble, challenging??? Quote:
The correct answer is 14. Quote:
http://en.wikipedia.org/wiki/Coin_problem also gives the solution, but it's probably harder to use that more powerful technique here.  
March 15th, 2010, 01:35 PM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,932 Thanks: 1127 Math Focus: Elementary mathematics and beyond  Re: 8th grade proble, challenging???
Problem 1: Labeling the faces a, b, c, d, e and f: abe + bce + cde + ade + abf + bcf + cdf + adf = 70 (e + f)(ab + bc + cd + ad) = 70 (a + c)(b + d)(e + f) = 70. Factors of 70: 2, 5, 7, 10, 14, 35. 
March 15th, 2010, 03:17 PM  #4 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: 8th grade proble, challenging???
Nice, Greg.

March 15th, 2010, 03:18 PM  #5 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,932 Thanks: 1127 Math Focus: Elementary mathematics and beyond  Re: 8th grade proble, challenging???
ty


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