In Escape the Museum After Dark you climb nine locked galleries, with Nib the mouse and Ada Quill, and the lock that sets this book apart is Timeline Rows. A row with a timeline tag goes up (or down) in equal steps, like the years along a museum timeline: 1900, 1910, 1920. Every brick is still the sum of the two below it.
What equal steps give you
If three bricks in a row are in equal steps, the middle one is exactly halfway between the other two. So when the ends are known, the middle is their average. Here is a made-up example.
A timeline on the bottom row
The bottom row carries a timeline tag and shows 6, a gap and 14. The top is 40.
Halfway between
Equal steps means the middle is the average of the ends: (6 + 14) รท 2 = 10. The steps are 4 each time.
Climb
6 + 10 = 16 and 10 + 14 = 24.
Check the top
16 + 24 = 40, the top we were given. And notice: 16 and 24 differ by 8, double the step of 4.
The doubling surprise
Here is the part that makes this lock fun. Every row above a timeline row is also a timeline, and its step is twice as big. Row 3 went up in 4s, row 2 goes up in 8s, and a row above that would go up in 16s. It works because each brick is a sum of two neighbours that both moved by the same step, so the sums move by two steps.
More about the book
The 45 chambers are nine galleries of five, going up through a museum cut open into three storeys, and there is a Golden Capstone mystery to solve. The Catalogue Board at the end of the book is a seven-row timeline board that uses what the locks taught you.
How a page looks in the book

A low-resolution page from Escape the Museum After Dark, so you can see the layout. Nothing on it is solved.
Books mentioned

Escape the Museum After Dark
A puzzle adventure gamebook: climb nine locked galleries to the Pyramid Hall by dawn, with 12 kinds of lock. Timeline Rows is one of them.
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