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?

D to _

ReplyDeleteC 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!

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

ReplyDeleteC 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.

I can not seem to understand it

ReplyDeletei have tried all what you said but they do not seem to add up

what could i have possibly done wrong?

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.

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

Mike's answer is right!

ReplyDeleteBrian C -- step 6 (B to __) is impossible, as it tells to move B backwards!

ABC_DEF

ReplyDeleteAB_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

It's fine, but can u try to write down the algorithmic pseudo code for this.

DeleteThank you!I've an homework to do this kind of algorithm!

i know the answer, now whats the formula?

ReplyDeletei know hot to do the puzzle, but what is the formula is algerbra terms?

ReplyDeleteIT IS EASY

ReplyDeleteBUT WOT IS THE FORMULA!?

easy.

ReplyDeletenumber 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.

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

ReplyDeletewhy does the minimum number of moves always seem to work out as one less than the square number sequence ie

ReplyDelete2 frogs->8 moves(9-1) , 3 frogs ->15 moves (16-1) 4 frogs ->24 moves (25-1)

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.

ReplyDeleteSo 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