145 Doors Puzzle

Can you solve the 145 Doors Puzzle to help a prisoner break out of a medieval dungeon with 145 doors?

The 145 Doors Puzzle is one of my favorite puzzles from The Moscow Puzzles: 359 Mathematical Recreations by Boris A. Kordemsky.

You can also find the 145 doors puzzle online at NCTM Illuminations.

Here’s the text of the puzzle: 

A prisoner was thrown into a medieval dungeon with 145 doors. Nine, shown by black bars, are locked, but each one will open if before you reach it you pass through exactly 8 open doors. You don’t have to go through every open door but you do have to go through every cell and all 9 locked doors. If you enter a cell or go through a door a second time, the doors clang shut, trapping you.

The prisoner (in the lower right corner cell) had a drawing of the dungeon. He thought a long time before he set out. He went through all the locked doors and escaped through the last, upper left corner one.

What was his route?

Fair warning: the author of this puzzle classifies this as a “Difficult Problem.”

I first used this puzzle with my students back in 2015 when I was doing Brain Teaser Tuesday. I gave the puzzle to my students in a dry erase pocket to make it easy to show (and correct!) their work.  

If you don’t have a classroom set of dry erase pockets, you could also use heavy duty sheet protectors. But, I highly recommend investing in a classroom set of the pockets since they are so much more durable.

My students really struggled with this puzzle and wanted to give up easily.  They were definitely not interested in persevering towards a solution which really made me sad.