Mathematics for Algorithms and Systems

Fall 2008
home/syllabusannouncementshomeworkextra credit

extra credit

  1. (assigned 9/29) What is largest value that cannot be formed using stamps with values r cents and s cents (where r and s have no common divisor greater than one). For example, if r = 3 and s = 5, then this least value is 7 (as we saw in class).

  2. (assigned 9/29) Is is possible to pack all the rectangles of side length 1/k by 1/(k+1), k=1, 2, 3,...., without overlap into a square of side length 1? Answering this question (with a proof!) will be worth $1000 to the first solver!