Riddles, one at a time
Gem Finder: The Gem Field
A number counts the gems in the 8 tiles around it; numbered tiles have none. Which lettered tile hides a gem?
Start with the 0 in the bottom-left corner.
B
The bottom-left 0 makes C empty. The 1 above it touches only B and C, so B holds the gem.
One Stroke: House
Without lifting your pen and without going over any line twice, which figure can you draw?
Count the lines at each dot. Odd dots must be the start or the end.
B
Only B has just 2 dots where an odd number of lines meet: start at one, end at the other.
Growing Diamond
Steps 6 and 7 are not shown. How many tiles will step 8 have?
Each diamond is two square grids of tiles, one a little smaller than the other.
113
Step 8 is an 8 × 8 grid woven with a 7 × 7 grid: 64 + 49 = 113 tiles.
Lamp Code: Deduce the Lamps
What number does the last row show?
Compare the rows showing 3 and 5: they share one lamp.
14
Lamps worth 8, 4, 2, 1 fit every row: 2 + 1 = 3, 4 + 1 = 5, 8 + 1 = 9, 4 + 2 = 6. So 8 + 4 + 2 = 14.
The Stone Garden
Which gate leads to the fountain?
GATE C
Every other gate is sealed off by a stone wall.
Shaded Part: The Triangle
What fraction of the square is gold?
Cut the triangle down the middle and move one half.
1/2
The triangle has the full base and full height of the square, so it is half: 8 of 16 squares.