# Crossing the River

by on May 25, 2012

Questions:
• On the weekend, friends of mine went camping. They were camping on a small island in the middle of the lake. There were eight adults and two children in all.
• When they went to cross the lake and return home their boat was missing. They searched and searched but all they could find was an old canoe. It wasn’t as big as the boat and they were worried it wouldn’t carry them all. So, they tested it and found the boat could carry either:
• • One or two children
• At first they thought some of them would be stranded forever, but finally, they figured out how to get them all safely across the lake.
• Can you figure it out?
• —————
• Repeat the problem using counters. I want to know the number of crossings it takes to shift the 8 adults and 2 children.
• —————
• What if one of the adults was sick and didn’t end up going camping? How would that change the number of crossing?
• —————
• Let’s adjust the number of adults. How does the number of crossings change when the number of adults changes? Record all your data. Can you find an algebraic pattern?

The first question, it gave me a bit of a hesitation, but after a while, I figured out a solution, and it is:

2 children goes across to the island, 1 child drops off, another goes back on, he drops off, an adult goes on, he drops off at the other side, the child left on the original island gets on and returens the child on the middle island back. Then the whole cycle repeats until everybody has crossed.

The second question, I thought it was the hardest among all, because I had to figure out how many crossings it takes for 8 adults and 2 children to get through an island. So eventually, I repeated the count and I have came up with the number 33. Later I have did the same for 7 adults and 2 children, and have came up with 29.

The third part, we had to choose 5 random numbers of adults. I chose 18, 23, 25, 3 and 1. Soon I figured out the algebraic pattern. It was 4y+1. With the function, I gradually  figured out the answers for the 5 numbers. Respectively, there were 73, 93, 101, 13 and 5.

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