Question 30
Liu and Lia play on the classroom board. One of them writes two positive natural numbers and the other has to perform MULTISUM transformations until the smaller one is transformed into the larger one. A MULTISUM transformation consists of replacing a number $a = m + n$ by $m \cdot n$; for example, we can replace $10$ by $2 \cdot 8 = 16$.
a) Liu writes $6$ and $15$ on the board. Show how Lia can transform $6$ into $15$.
b) Lia writes $5$ and $2019$. Show how Liu can make the transformation.
c) The teacher liked the game and decided to join in, writing $7$ and $x$, and asked how many possible values of $x$ there are such that $7$ can be transformed into $x$ with exactly two MULTISUM transformations. What should Liu and Lia's answer be?
a) Liu writes $6$ and $15$ on the board. Show how Lia can transform $6$ into $15$.
b) Lia writes $5$ and $2019$. Show how Liu can make the transformation.
c) The teacher liked the game and decided to join in, writing $7$ and $x$, and asked how many possible values of $x$ there are such that $7$ can be transformed into $x$ with exactly two MULTISUM transformations. What should Liu and Lia's answer be?