Riddles, one at a time
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.
Mirror Odometer: 15951
How many more km until the next mirror number?
The middle digit is already 9, so it cannot go up. What has to change instead?
110 km
The next mirror number is 16061: 16061 − 15951 = 110.
Hands Apart: 2:20
What is the SMALLER angle between the hands?
In 20 minutes the hour hand moves 10° past the 2.
50°
Minute hand at 120°, hour hand at 60° + 10° = 70°: 50° apart.
How Many Routes: 3 × 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.
10
The two corners next to the gem can be reached in 6 and 4 ways: 6 + 4 = 10.
Move One Rod
Move exactly one rod. What is the true equation?
9 − 8 = 1
The top rod of the 7 turns the 3 into a 9.