# Problem Solving – 15 Door Puzzle

15 Door Puzzle – You must shut all the doors on the ground floor of the castle without going through any door twice. It is a bit harder than it seems.

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# Classroom Problem Solving

## 15 Door Puzzle

Classroom Problem Solving

### Problem Solving:

Here’s a challenging puzzle to use as a classroom poster or a fun addition to homework.

The ground floor of this castle has 15 doors. Each night before bed you must shut all the doors without going through any door twice. You may start either inside or the outside and once you pass through a doorway it is considered shut.

### Things to Think About & Test Out:

– Should I start on the outside?
– Should I start on the inside?
– Should I start in a room with an even number of doors?
– Should I start in a room with an odd number of doors?
– How will I record where I’ve been? Do some people place a counter over each door they’ve traveled through? Might this work for you? Think of a ‘better’ way to record your path?
– Think about how to use the numbers above the door to record your path?
– How will you record the room you started in? How will you record if you started on the outside of the puzzle?
– Since there are many ways to solve this puzzle some people have written a letter on the floor of each room and then the number sequence of doors they go through to solve the puzzle. Test this idea out and see if this works for you.

Problem Solving Puzzle

### Notes from the Publisher:

– I have often wondered if it is possible to start in one room, close all doors and finish in the room I started in i.e. can you start in your bedroom, shut all the doors and finish back in your bedroom. After a long time trying I am yet to find a way. Give it a try and see if you have better luck.

– I have also thought about this house being located in a rainy country. If it was me, when it was dark, cold, and wet I would not want to travel long distances outside the building i.e I would try to avoid running outdoor 5 and indoor 15.

Are there solutions where the person spends a shorter time outside?

### Wall Display Ideas:

Display the A4 version of the puzzle on a classroom wall. Below it places a blank piece of paper and a pencil. Once the students work out a possible solution they record their path using letters and numbers from the puzzle. This way other students can see and verify solutions by tracing the path plus they can also see if their solution has already been discovered. When using this method I find students like to sign their work for all to see 🙂
I also place these puzzles on the windows of my classrooms facing the halls and on the classroom door. I am always surprised by how much attention they draw.

1/2 A4 size is ideal for Math Centres. I tend to print out enough for each student in the group.

### Scratch Version:

Since there are so many ways to solve this puzzle it can get messy. For this reason, I have included black-and-white line versions of the puzzle to experiment with.  I have had success in my classrooms having students use a variety of colored pencils to record the paths they have taken and their solutions.

### Computer Version

Included in this download is a small puzzle graphic. I have students open it in a program like Paint or PhotoShop. They then choose a pencil or brush tool and draw the paths they are taking. Students use CTRL  and Z to undo their unsuccessful tries.