12. On the table there is a tower made of blocks numbered from 1 to 90 , as shown on the left of the diagram. Yett takes blocks from the top of the tower, three at a time, to build a new tower, as shown on the right of the diagram. How many blocks will be between blocks 39 and 40 when he has finished building the new tower?
A 0
B 1
C 2
D 3
E 4
Solution
$\mathbf{E}$

If $n$ is divisible by 3 , then block $n$ will be be moved with the two blocks underneath it, $n-1$ and $n-2$.

Since 42 is divisible by 3 , block 42 will be moved with blocks number 41 and 40 underneath block 42. So now our new tower from top down looks like: $42,41,40,45,44, \ldots$.
Yett would then next move the three blocks that are on the top of what remains of the original tower, namely 39,38 and 37 . Adding these to our previous set gives the order as: 39, $38,37,42,41,40,45,44, \ldots$

It follows that between blocks with numbers 39 and 40 there will be 4 blocks.