## 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.

Ø | 1 | 2 |
3 | 4 | 5 |

6 | 7 | 8 |
9 | A | B |

C | D | E |
F | G | H |

I | J | K |
L | M | N |

O | P | Q |
R | S | T |

U | V | W |
X | Y | Z |