A pattern of tiles repeats: black, black, white. What colour is the 100th tile?
Hints
Take them one at a time. The first gives nothing away.
1A nudge
The pattern repeats every three tiles.
2The strategy
Divide the position by the length of one repeat and keep the remainder, not the answer. The remainder tells you how far into a fresh repeat the tile sits.
3The full solution
100 divided by 3 is 33 remainder 1, so tile 100 is the first tile of a repeat, which is black.
Solution— no shortcut on this one
One repeat is three tiles: position 1 black, 2 black, 3 white. Divide 100 by 3 to get 33 remainder 1, so 33 whole repeats use 99 tiles and tile 100 is the first of the next repeat - black. Careful: a remainder of 0 would mean the last tile of a repeat, which is white. The transferable idea: the remainder gives the position inside the cycle, and remainder zero is the end of a cycle, not the start.
Why this is on the test: Cycle questions turn a huge position into one division, and reading the remainder is where the mark is won or lost.