Yawns are catching, and so is the lock called Catching Yawns in Escape the Sleepwalking Town. Its rule: every brick is the two bricks below it added together, but a brick wearing a ×2 yawn badge is counted twice. Doubling goes up. Halving comes back down.
A made-up example
The top is 28. The bottom row is 3, a missing brick and 5. The missing brick wears the yawn badge, so it counts twice wherever it is added.
What we know
Top 28, bottom 3, ? and 5. The middle bottom brick yawns, so it is counted twice.
Build the middle row with the missing brick
The left middle brick is 3 + the yawner counted twice. The right middle brick is the yawner counted twice + 5. Call the yawner x: 3 + 2x and 2x + 5.
Count it again at the top
The top is (3 + 2x) + (2x + 5) = 8 + 4x. The yawner is counted four times in all: twice in each middle brick.
Take away the known and halve twice
28 − 3 − 5 = 20. That is four yawners. Halve it: 10. Halve again: 5. The yawner is 5.
Check
3 + 5 + 5 = 13 and 5 + 5 + 5 = 15 (the yawner counted twice each time). Then 13 + 15 = 28.
Halving in your head
Halving is easier than it looks if you split the number into friendly parts.
- Halve tens and ones separately. Half of 74: half of 70 is 35, half of 4 is 2, so 37.
- Halve hundreds first. Half of 136: half of 100 is 50, half of 36 is 18, so 68.
- Halve twice for a quarter. A quarter of 20 is half of 10, which is 5.
- Check by doubling. 37 doubled is 74. Always true.
How a page looks in the book
A low-resolution page from Escape the Sleepwalking Town, so you can see the layout. Nothing on it is solved.
Books mentioned
Escape the Sleepwalking Town
A comic puzzle adventure gamebook up nine locked streets to the Wake-Up Pyramid, with 15 kinds of lock and true sleep facts. Catching Yawns is one of them.
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