## An Interesting Way to Combine Numbers

Topic Classification: nid, "Topic Classification"); ?> Tags: nid, "Problem Tag");?>

1-2

3-4

5-6

7-8

9-10

11-12

13-14

In this Joshua Zucker and Tom Davis lesson plan that explores varying approaches for different skill levels to the problem:

Imagine that all the numbers from $1$ to $100$ inclusive are written on the blackboard. At every stage, you are allowed to erase two numbers that appear on the board (let’s call the numbers you erased $x$ and $y$) and in place of the two erased numbers, write the number $x+y+xy$. Repeat this operation until only a single number remains.

What are the possible values for that remaining number?