Number of frogs: 🔊 🔇

Can you do it with 3 blue frogs and 3 green frogs?

Does it always take the same number of moves?

How about with a different number of frogs?

Can you find a rule for the number of moves?

Investigate..

The instructions for this investigation were kindly made available by:

D.Keith www.subtangent.com

You can earn a very prestigious Transum Trophy for the work you do for this investigation. If you can complete the table below then a virtual trophy will be awarded to you. When you have worked out the numbers in the first few rows you may be able to spot a pattern (it's not simple) which will help you fill in the other rows.

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Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

John from Transum,

Friday, January 21, 2022

"This really is one of the old-school investigations. I remember in the early eighties, when investigations suddenly became a 'thing', this was one activity that I did in the classroom with pupils acting as the frogs sitting on a row of chairs arranged at the front of the classroom. There have been a number of computer-based versions over the years and I'd been using a Flash version on Transum but now that Flash has been banished from browsers this is an updated version in JavaScript.

The basic part of the investigation will reveal a number sequence but can you find the rule for the nth term? The investigation can be extended with unequal numbers of blue and green frogs or different numbers of lily pads."