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