Problem of the Week
Problem E and Solution
The Third Escape

Problem

Ingrid, Jayant, Neela, and Radko each brought a group of friends to POTW Escape. Each group completed a different escape room: Lost Shoes, Memories, Dollhouse, or The Old Office. Each of the rooms had a different-coloured door: black, orange, purple, or yellow. The four groups all started at the same time, but finished at different times.

Use the clues below to match each group with the name of their escape room, the colour of its door, and the order in which they finished.

1. The group that completed Memories finished before Ingrid’s group, but after the group that went through the black door.

2. Neela’s group finished immediately after the group that completed Lost Shoes.

3. The group that went through the yellow door finished immediately before the group that went through the purple door.

4. The group that completed Dollhouse went through the orange door and did not finish last.

5. Radko’s group did not finish third and did not go through the orange door.

6. Jayant’s group did not go through the yellow door.

Solution

First we will look at the door colours. From clue (1) we learn about three groups. Of these groups, the group that went through the black door finished before the other two. This tells us that the group that went through the black door finished either first or second. Clue (3) tells us that the group that went through the yellow door finished immediately before the group that went through the purple door. Clue (4) tells us that the group that went through the orange door did not finish last. Putting these together gives the following two possibilities:

1. The group that went through the black door finished first. Then the group that went through the orange door must have finished second, followed by the group that went through the yellow door, and finally the group that went through the purple door.

2. The group that went through the black door finished second. Then the group that went through the orange door must have finished first, the group that went through the yellow door finished third, followed by the group that went through the purple door.

From clue (4), the group that went through the orange door completed Dollhouse. Then from clue (1), the group that went through the black door finished before the group that completed Memories, which finished before Ingrid’s group. For each possibility there is only one way to place these. We summarize what we know so far for each of these possibilities in the following tables.

Possibility 1:

Possibility 2:

From clue (5), since Radko’s group did not finish third and did not go through the orange door, we can conclude Radko’s group went through the black door. From clue (6), since Jayant’s group did not go through the yellow door, we can conclude Jayant’s group went through the orange door. It follows that Neela’s group went through the yellow door. We summarize what we know so far for each of these possibilities in the following tables.

Possibility 1:

Possibility 2:

Finally, from clue (2) we know Neela’s group finished immediately after the group that completed Lost Shoes. We can now eliminate possibility 1. It follows that the group that completed Lost Shoes finished second. Then the group that completed The Old Office finished last. The completed table is shown.