Riddles, one at a time
Three Turning Rings
At which step number are all three gems at the top again?
36 STEPS
Notches 9, 6 and 4: the first common multiple is 36.
How Many Routes: 2 × 2 Grid
Moving only right or up, how many different routes lead from start to the gem?
Each corner's count is the count to its left plus the count below it.
6
Add the ways from the left and from below: 3 + 3 = 6.
Flip-Flop Gates
Gates start as shown and flip after each box. Where does box 3 land?
BIN C
After boxes 1 and 2, box 3 goes left, right, right.
Shaded Part: Tilted Square
What fraction of the square is gold?
Find the area of the four corner triangles that are not gold, then take it away.
5/8
The 4 corner triangles are 3 × 1 ÷ 2 each: 6 of 16 squares. Gold is 10/16 = 5/8.
Turn, Flip, Turn
Which card do you get?
Mark one corner of the card and follow it through each step.
A
Turn, flip top-bottom, turn: the same as one top-bottom flip. A.