So how does the binary trick work?
One must take the tiles.
You might notice some patterns in each of the tiles. Each has its own interesting set of patterns, both in each row and in each column.
Most importantly, the relationship of the tiles to each other.
The upper left number in each tile just happens to be a power of two!
In fact, if we convert the tiles into binary, what happens?
You might notice there is a patter for each power of two! So when a students answers yes or no if a number is on a given tile, they are actually telling you if they digit is used to create that given number in binary.
For instance the number 13 in binary is 01101
So this number appears on the tiles for 1, 4, and 8, but does not appear on 2 or 16.
You do not need to actually convert your number into binary. You could just add up the numbers in the left hand corner of each tile!