p10. Three rectangles of dimension X×2 and four rectangles of dimension Y×1 are the pieces that form a rectangle of area 3XY where X and Y are positive, integer values. What is the sum of all possible values of X?
p11. Suppose we have a polynomial p(x)=x2+ax+b with real coefficients a+b=1000 and b>0. Find the smallest possible value of b such that p(x) has two integer roots.
p12. Ten square slips of paper of the same size, numbered 0,1,2,...,9, are placed into a bag. Four of these squares are then randomly chosen and placed into a two-by-two grid of squares. What is the probability that the numbers in every pair of blocks sharing a side have an absolute difference no greater than two?
PS. You should use hide for answers. Collected [url=https://artofproblemsolving.com/community/c5h2760506p24143309]here. Stanford Math Tournamentnumber theoryalgebracombinatorics