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10292007  #71 
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Yeah, a Platonic solid.

10302007  #72 
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My attempt.
You know that the surface area of the tetrahedron is , making the side length . This gives the volume: You all may laugh at this failing attempt. 
11012007  #73 
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Next problem?

11022007  #74 
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Wait is that right?
If , what is ? 
11032007  #75 
Join Date: Oct 2006
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, it's 18.
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11042007  #76 
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Okay, so here's the next one:
The 9digit number abb,aba,ba3 is a multiple of 99 for some pair of digits a and b. What is b  a ? 
11042007  #77 
Join Date: Oct 2006
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Using properties for divisibilities by 9 and 11, we determine
a+b is 6 mod 9 ba is 4 mod 11. Since they are digits, ba is 4.
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11052007  #78 
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Good.
What is the smallest multiple of 24 that is a perfect cube? 
05132008  #79 
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(x+y)^6
Using Pascal's triangle, we could figure out the problem x^6 + 6*x^5*y + 15*x^4*y*2 + 20*x^3*y*3 + 15*x^2*y^4 + 6*x*y^5 + y^6 Do you notice a pattern? 
05132008  #80 
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first, you factor 24 = 2^3 * 3
So the next perfect cube would be 2^a multiple of three * 3^3 The answer is 24 * 9, which is equal to 216 next question: WITH FULL SOLUTIONS PLEASE Fractions a/b and c/d are called neighbor fractions if their difference (ad  bc)/(bd) has a numerator of positive or negative 1, that is, ad  bc = positive or negative one. Prove that If a/b and c/d are neighbor fractions, then (a + b)/(c + d) is between them and is a neighbor fraction for both a/b and c/d; moreover, no fraction e/f with positive integer "e" and "f" such that f is less than b + d is between a/b and c/d. [/img] 
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