Back to Square One
This time Mr. and Mrs Smith planned to go around a square track ( remember the pentagon problem). While Mr. Smith runs one side of the square, Mrs. Smith; being young, completes two sides and a diagonal in the same time.
One morning Mr. Smith decided to test Mrs Smith's intelligence. He said "I will cover all four sides of the square and you cover all the tracks twice (all sides and two diagonals). We must start from the same corner and in the same direction and must finish together, moving in the same direction again." Mr. Smith added. "I will only tread my foot on a path which you have already taken and I don't want you to meet me anywhere en-route".
Assume ABCD is the square, can you help Mrs. Smith route the path?
One morning Mr. Smith decided to test Mrs Smith's intelligence. He said "I will cover all four sides of the square and you cover all the tracks twice (all sides and two diagonals). We must start from the same corner and in the same direction and must finish together, moving in the same direction again." Mr. Smith added. "I will only tread my foot on a path which you have already taken and I don't want you to meet me anywhere en-route".
Assume ABCD is the square, can you help Mrs. Smith route the path?
Labels: friday special, mathemagic, puzzle
posted by Rajesh Lal at
8:21 PM
7 Comments:
ok so the square is
B--------C
I I
I I
I I
A--------D
Mrs smith goes A-B, B-C, C-A
Mr smith goes A-B
Mrs smith goes A-C, C-D, D-A
Mr smith goes B-C
Mrs smith goes A-B, B-C, C-A
Mr smith goes C-D
Mrs smith goes A-C, C-D, D-A
Mr smith goes D-A
this means that they both meet and point A heading west [or in this diagram from D to A] at the same time
=>> Daniel
Thats a good one! I understood the question as there being 2 crossing diagonals, forming an X in the middle of the square, rather than only the one from A-C, which you did 2 times back and forth. This is what i got:
him: A-B
her: A-B-C-A
him: B-C
her: A-D-C-A
him: C-D
her: A-B-D-C
him: D-A
her: C-B-D-A
So they both start from A going to B, and both finish from D going to A. The only condition that my way does not satidfy is that in Mr. Smith's C-D run, Mrs Smith crosses him going on the oposite direction, which cant be. I will keep working on it, and correct my answer if need be. :)
Val D.
(I'm Anonymous Joe)
Him: A-B
Her: A-C-B-A
Him: B-D
Her: A-B-C-A
Him: D-C
Her: A-D-B-D
Him: C-A
Her: D-C-B-A
him: A-B
her: A-B-C-D
him: B-C
her: D-A-C-D
him: C-D
her: D-B-C-A
him: D-A
her: A-B-D-A
Lesley said...
him: A-B
her: A-B-C-D
him: B-C
her: D-A-C-D
him: C-D
her: D-B-C-A
him: D-A
her: A-B-D-A
May 29, 2008 4:36 AM
Anonymous Joe replied:
No, that cannot be. since you have him going from A to B to C to D, I take it that your square has A in top left, B in top right, C in bottom right, and D in bottom left. Therefore, on her first move you have her walking completely around the square, insead of two sides and one diagonal.
Anonymous Joe again -- I didn't mean to say "completely around the square"; I meant around three SIDES of the square, rather than two sides and a diagonal.
And after I posted, I realized that the square you are using is based upon the first post in this thread. The solution I proposed used a slightly different square:
A-----B
| |
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C-----D
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