Leap Frog Investigation

Briony was surfing the internet for an interactive maths activity. She found the Leap Frog Investigation and is challenging you to move the Green and Blue frogs to opposite sides of the pond.

Stage 3 Level
Set the sliders at the top of the Leapfrog webpage to:
B B B B _ G G G G (4 frogs on either side).
Or
B B B B B _ G G G G G (5 frogs on either side).

Blue frogs can only move to the right
Green frogs can only move to the left. Frogs can jump over only ONE frog at a time.
Frogs can move to a blank space.

Record the moves you have taken.
How many moves does it take to move the frogs?
What strategies did you use to move the green frogs to the left and the blue frogs to the right?
What did you find out?

Feature Solution

The feature solution for the Leap Frog Investigation problem came from Ange and Sarah from Candelo PS

What did you have to find out?
How to make the blue frogs move to the right side of the pond and the green frogs to the left side of the pond.

What materials did you use?
A laptop, some writing paper and our logic and skills.

How did you think? What strategies did you use? How did you solve this problem?
We thought smartly. Our first strategy was to make sure that a blue frog would never touch another blue frog, and a green frog would never touch another green frog. Then by moving a line of one colour frogs over the other colour and repeating this method. Finally the same colour frogs will meet up at the opposite side of the pond.

What answers did you come up with?
The coordinates for moving 4 frogs was: FE, DF, CD, EC, GE, HG, FH, DF, BD, AB, CA, EC, GE, IG, HI, FH, DF, BD, CB, EC, GE, FG, DF, ED ending in 24 moves.

Also for 5 frogs: GF, EG, DE, FD, HF, IH, GI, EG, CE, BC, DB, FD, HF, JH, KJ, IK, GI, EG, CE, AC, BA, DB, FD, HF, JH, IJ, GI, EG, CE, DC, FD, HF, GH, EG, FE ending in 35 moves.

We also tried using 5 and 6 frogs using the same strategy but with counters ending with 41 moves.

After a lot of practice and working out we figured out a way to easily figure out how many moves you get from any amount of frogs, such as if you had 8 blue frogs and 7 green frogs to figure it out you times the 2 numbers of frogs (8x7) which equals 56 (moves), then you add the two numbers of frogs (8+7) which equals 15 (moves), then add the 2 final numbers together (56+15) which equals 71 moves as the final answer. This method will work for ANY amount of frogs.

Also we (Sarah) have sent you 2 movies of the frogs hopping our answers to 4 frogs on either side and 5 frogs on either side.