Escape the Sunken Pyramid takes you up a spiral ramp through nine sunken levels of a deep-sea station, and its new lock is Sonar Echoes. In the book's words: some bricks carry a sonar buoy instead of a number. The buoy shows the gap between the two bricks under it, and its arrow points to the bigger one. Every brick is still the sum of the two below it.
A gap and a sum make a pair
A gap alone does not tell you two numbers: 7 and 11 differ by 4, and so do 20 and 24. A sum alone does not either. But the sum and the gap together pin both numbers down. That is the whole trick of this lock. Here is a made-up example, a little easier than the book's locks.
A top, a brick and a buoy
The top is 40. The right brick of the middle row is 22. The left brick of the middle row wears a buoy: the gap between the two bricks under it is 4, and the arrow points to the right one.
Find the buoy's brick
The top is the sum of the two middle bricks. 40 − 22 = 18, so the buoy brick is 18.
Use the gap
The two bricks under 18 add up to 18 and differ by 4. Take the gap off, 18 − 4 = 14, and halve it: the smaller brick is 7. The bigger is 7 + 4 = 11, and the arrow said the bigger one is on the right.
Finish the row
The right middle brick is 22 and its left neighbour below is 11, so the last brick is 22 − 11 = 11. Check: 7 + 11 = 18, 11 + 11 = 22, 18 + 22 = 40.
The pattern to remember
- Two bricks, their sum and their gap: the smaller one is (sum − gap) ÷ 2, the bigger one is the smaller plus the gap.
- Look for the sum first. A buoy sits on a brick, and that brick's number is often something you can already work out.
- Follow the arrow. It says which of the two is the bigger. Swap them and everything above is wrong.
More about the book
The 45 chambers are nine levels of five, going up a square-spiral ramp, and the map is the pyramid seen from above. Every lock in the book has a rule card, hints and full solutions in the back. Sonar Echoes is the one lock you will not find in an ordinary number pyramid.
How a page looks in the book
A low-resolution page from Escape the Sunken Pyramid, so you can see the layout. Nothing on it is solved.
Books mentioned
Escape the Sunken Pyramid
A puzzle adventure gamebook: climb nine sunken levels through 45 locked chambers, with 12 kinds of lock. Sonar Echoes is one of them, so the book is not all buoys.
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More field notes
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Solve the puzzle, read the door brick, turn to that page. Here is the whole game in three moves, with a worked example.
Tool Doors: How the Inventory Works in Escape the Giant's Castle
Six castle mice lend you numbered tools, and some doors open only when you add a tool's number. Learn the new rule with a drawn, step-by-step example.
Better Ways to Learn Addition and Subtraction
Flashcards have their place, but understanding comes first. Five friendly strategies, drawn step by step, plus how puzzles make the practice stick.
How to Solve a Number Pyramid, Step by Step
Two moves are all you need: add up and subtract down. Follow one real puzzle from the first brick to the top, with every step drawn.