On the Subject of Integer Trees

Don’t you think it’s a bit weird that tree diagrams are generally sideways or inverted, almost never in the same orientation as physical trees?

  • In the top-left there’s two input integers, referred to as p (on top) and q (on the bottom). Both must be given a tree.
  • The tree structure for p corresponds to the first character in the serial number in the table below.
  • To put integers in the tree, find the largest single-digit number n which divides evenly into p. Then, divide p by n (p becomes this new value) and place n into the first unfilled (hollow) node of the tree in reading order. Repeat this process until all unfilled nodes have an integer in them.
  • Find the integer tree for q following the same procedure, using the second character in the serial number for the structure instead.
  • To determine your answer, create a new tree (with no filled nodes) where each node contains the absolute difference between the numbers in that position within the other two trees. Treat nodes without digits as zeros. The number you must submit is the product of all non-zero digits in this tree multiplied by the number of positions with digits in neither of the input trees.
  • Use the up arrows to increment individual digits and the right arrow to submit your answer. Upon an incorrect submission the answer will not change.
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