Through-the-Looking-Glass Monsters

MonstersHere is a funny puzzle from Kvant (1996, vol 4), the best Russian journal of recreational math.

When Alice goes through the looking-glass, she might meet many multi-headed, multi-armed, multi-legged beings. A being with H heads, A arms and L legs is considered:

  • smart, if H > A+L,
  • strong, if A > H+L,
  • fast, if L > H+A.

Can there exist a well-rounded personality behind the looking-glass: someone who is smart, strong and fast at the same time?


One Comment

  1. Tipa:

    If, in the Looking Glass World, creatures have no trouble having negative extremities, than a beast with -1 heads, arms and legs will be smart, strong and swift.

    If they have to have positive extremities, than it is impossible, as there is no H, A and L where all are positive integers and both A-L > H and L-A > H are true.

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