Riddles, one at a time
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.
Split 8 Litres
Fewest pours to share it 4 L and 4 L?
Only the 8 L and 5 L jugs can end with 4 L. Use the 3 L jug as a measure.
7 pours
8→5, 5→3, 3→8, 5→3, 8→5, 5→3, 3→8: 4 L and 4 L.
The Stone Garden
Which gate leads to the fountain?
GATE C
Every other gate is sealed off by a stone wall.
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.
How Many Routes: Pass the Lantern
Moving only right or up, how many routes from start to the gem pass the lantern?
Count the ways to the lantern, then the ways from it to the gem, and multiply.
36
6 ways to the lantern, then 6 ways on: 6 × 6 = 36.