Thursday, July 20, 2006

Leap Frog

I can never remember how to do this. I always have to work it out every time I see it.

You have six frogs trying to cross the stream. On the first three stones, there are three frogs (A)lex, (B)obby, and (C)arl. On the other side of the stream are three more frogs, on three more stones. Their names are (D)eb, (E)nid, and (F)rancine.

So, when they start, they look like this:
A B C _ D E F

There's an empty stone in the middle. A, B and C want to get to the side D, E and F are on and vice-versa. But none of the frogs want to get wet today. Each frog can leap-frog over another frog (if they are of the opposite sex) or can jump to an empty stone that's next to them. How do you get them to switch sides?

Did I explain that well enough?

14 comments:

  1. D to _
    C ju D
    D to _
    B ju D
    D to _
    B to _
    E ju C
    F to _
    C ju F
    B ju E
    A ju D
    D to _
    E ju A
    F ju B
    B to _
    A ju F
    F to _
    And there you go!

    ReplyDelete
  2. Brian, your answer and mine seem to line up. Thanks for answering!

    C steps, D hops over her. E steps, C hops, B hops, A steps, D hops, E hops, F hops, C steps, B hops, A hops, E steps, F hops, and A steps. That's 15 moves altogether.

    ReplyDelete
  3. I can not seem to understand it
    i have tried all what you said but they do not seem to add up

    what could i have possibly done wrong?

    ReplyDelete
  4. I'm not sure what could be wrong. Keep in mind that A, B and C are always moving to the right, while D, E, and F are always moving left.

    Also, if they hop, then they are moving two spaces (jumping over the occupied space) and if they step, then they only move one spot.

    ReplyDelete
  5. Mike's answer is right!
    Brian C -- step 6 (B to __) is impossible, as it tells to move B backwards!

    ReplyDelete
  6. ABC_DEF
    AB_CDEF
    ABDC_EF
    ABDCE_F
    ABD_ECF
    A_DBECF
    _ADBECF
    DA_BECF
    DAEB_CF
    DAEBFC_
    DAEBF_C
    DAE_FBC
    D_EAFBC
    DE_AFBC
    DEFA_BC
    DEF_ABC

    ReplyDelete
    Replies
    1. It's fine, but can u try to write down the algorithmic pseudo code for this.
      Thank you!I've an homework to do this kind of algorithm!

      Delete
  7. i know the answer, now whats the formula?

    ReplyDelete
  8. i know hot to do the puzzle, but what is the formula is algerbra terms?

    ReplyDelete
  9. IT IS EASY
    BUT WOT IS THE FORMULA!?

    ReplyDelete
  10. easy.

    number of frogs on the right * number of frogs on the left, + number of frogs on the right, + number of frogs on the left. this gives you the minimum number of moves for the given situation.

    ReplyDelete
  11. Can you give a general statement which explains how to work out the number of jumps if you know the number of frogs.

    ReplyDelete
  12. why does the minimum number of moves always seem to work out as one less than the square number sequence ie
    2 frogs->8 moves(9-1) , 3 frogs ->15 moves (16-1) 4 frogs ->24 moves (25-1)

    ReplyDelete
  13. Just helped my daughter with this. I think the method is all around the pattern of the moves. The moves can either be slides (S) where the frog moves into the adjacent space or jumps (J) where the frog jumps over its neighbour into the space. If we think of Green (G) frogs on the left and Brown (B) frogs on the right then the pattern is simply an increasing then decreasing number of jumps, separated by slides.

    So for four frogs the pattern is

    GS
    BJ
    BS
    GJ
    GJ
    GS
    BJ
    BJ
    BJ
    BS
    GJ
    GJ
    GJ
    GJ
    BS
    BJ
    BJ
    BJ
    GS
    GJ
    GJ
    BS
    BJ
    GS

    A symmetrical pattern or palindrome

    ReplyDelete

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