Family Math #4
Fabulous Frogs
Across a stream is a row of seven stepping stones. On one side of the stream sitting on the first three stones are three female frogs, Fergie, Francine, and Freda. They all want to get to the other side. There is an empty stone in the middle. On the other side of the empty stone are three male frogs who want to get to the opposite side of the stream. Their names are Frank, Fred, and Frodo.
Only one frog can move at a time. Any frog may hop on the next stone if it is empty, or may hop over one frog of the opposite gender onto an empty stone.
What is the fewest number of hops that can happen to get everyone to the opposite side of the stream?
The Questions:
- What is the fewest number of hops needed? What is the order of those hops?
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The fewest moves are in 15 (fifteen) moves.
The order of the movements are: Male Slide, Female Hop, Female Slide, Male Hop, Male Hop, Male Slide, Female Hop, Female Hop, Female Hop, Male Slide, Male Hop, Male Hop, Female Slide, Female Hop, Male Slide.
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- Which family member did you work with? Is there a reason why you chose that family member?
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I worked with my Mom, we like to work together.
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- How did you go about solving the problem? In other words, what did you try first? What did you try next? Did you use coins to help you? Who offered suggestions? (This should be at least three sentences long and include your process)
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We found some plastic coins in two different colors representing the male and the female. We then moved them across seven boxes on a piece of paper, which we drew out, and counted the moves until we had success. It took a few tries to accomplish this. We moved the pieces across following the rules. Then we had to do it again to make sure our counts were right. Then we had to do it again to get the moves right to answer question number 1. Both if us had different suggestions on how to move the pieces to get the puzzle done fast and right.
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- Did you try anything that didn’t work? If so, what was it (be specific)
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Yes, we tried to draw it out in a picture and then draw lines for the movements and X out the pieces. But it was hard to know where the pieces were and how many moves we had made. Then we tried drawing many rows of seven stones and showing the different positions we moved the pieces in by row, in each row, but that was too hard to follow too. Since we made mistakes we had to erase a lot.
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- What did you enjoy most about this process and what did you find to be the most challenging or frustrating (be specific).
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We both enjoyed watching each other try to make the moves work. We also enjoyed solving the problem.
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