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Circus Bears

Question

At a circus there was a stunt completed by six bears, 3 brown, and 3 black.  Initially, the 3 brown bears were each standing in a square to the left of a center square and the 3 black bears were located right of center.  The bears either scooted left/right one square or one of the bears jumped over another until each group of bears were on the other group's set of squares.  If the bears needed 15 moves (scoots, jumps) to completely switch sides, how many scoots and how many jumps were used?  Bonus points: what is the largest total amount of bears (assuming equal amounts of brown and black bears) that could complete this task in fifteen moves?

Start: br br br ___ bl bl bl

End: bl bl bl ___ br br br

 

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2 answers to this question

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First question:

 

L = bLack, R=bRown

oops, I lined them up on the wrong side, sorry

LLL-RRR, LL-LRRR, LLRL-RR , LLRLR-R 

LLR-RLR , L-RLRLR, 

-LRLRLR, RL-LRLR, RLRL-LR, RLRLRL-

RLRLR-L, RLR-RLL, R-RLRLL, RR-LRLL

RRRL-LL, RRR-LLL

4 scoots, 11 jumps

 

Edited by CaptainEd
Add counts for scoots and jumps

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Oops, scoots/jumps count adjustments and comment on bonus question

6 scoots, 9 jumps

Average distance 4. If there were 8 bears total, they’d need to move an average of 5. That would require 20 jumps. So 6 bears is the max.

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