<p>A square pyramid and a tetrahedron have all of their edges equal to 1. A triangular face of the tetrahedron is glued to a triangular face of the pyramid. How many faces does the resulting solid have?</p>
<p>5 Faces.</p>
<p>Can you help me out with this question:</p>
<p>What is the product of the smallest prime number that is greater than 50 and the greatest prime number that is less than 50?</p>
<p>@Jack If 2009=9 mod n, then 2000=0 mod n. So the values of n allowed are all factors of 2000 that are greater than 9. There are 20 factors of 2000 and 5 of them are <=9 (1,2,4,5,8) so there are 15 values of n that work.</p>
<p>@flower: smallest prime number greater than 50 is 53, greatest prime number less than 50 is 47. The product 47*53=(50+3)(50-3)=2500-9=2491</p>
<p>@flower161</p>
<p>The smallest prime number that is greater than 50 is 53
While the greatest prime number that is less than 50 is 47
So their product is 53*47 = 2491</p>
<p>Darn, the pyramid/tetrahedron problem was too easy. </p>
<p>A slightly harder problem that I made up:
How many ways can one distribute 20 balls into four labelled boxes A,B,C,D such that each box has an odd number of balls?</p>
<p>@rspence
The answer is 36?</p>
<p>I could be wrong, but I obtained an answer greater than 36. Note that the boxes are labelled, and therefore distinguishable.</p>
<p>I’ll keep working on it when I get more time, but I only got the obvious result that it is the coefficient for x^20 of (x+x^3+…+x^19)^4.</p>