Trick-or-Treat Route POW

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Math Forum -Problem of the Week

Trick-or-Treat Route [Problem #410]

Mrs. Anderson told her son Todd that he was going to have to take his little sister, Grace,
trick-or-treating around their neighborhood on Halloween night. His mother agreed that he
only had to take her to four houses, and then he could go out with his friends.

Todd wants to plan ahead, so today his friend Joe helped him create a map of the
neighborhood with all the houses he must visit with Grace.


Next they made a list of the time it took them to walk between each two houses.


Anderson to Bader ----5 minutes
Anderson to Campbell ----9 minutes
Anderson to Daily ----6 minutes
Anderson to Elliot ----10 minutes
Bader to Campbell ----12 minutes
Bader to Daily ----11 minutes
Bader to Elliot ----5 minute
Campbell to Daily ----6 minutes
Campbell to Elliot ----4 minutes
Daily to Elliot ----8 minutes

When Grace saw what Todd was doing, she decided to plan her own route to maximize the
time she will be out trick-or-treating.

Find the answers to each of the following questions. Remember that in each case they
must start and end at the Anderson house.


How many different routes could the children take?

What is the shortest route based on the times given?
What is the longest route based on the times given?