It does not matter how many ways you can have the lines go from first
column to the second simulatneously. AD is AD whether it is "paired"
with BE/CF or BF/CE. All that matters is the number of combinations
of items in the first column with items in the second column.
Using just your 2 columns, you can have 9 lines -- AD, AE, AF, BD, BE,
BF, CD, CE, CF.
If we make it a 3 column game, we get 27 possible lines:
A D G
B E H
C F I
ADG, ADH, ADI, AEG, AEH, AEI, AFG, AFH, AFI, BDG, BDH, BDI, BEG, BEH,
BEI, BFG, BFH, BFI, CDG, CDH, CDI, CEG, CEH, CEI, CFG, CFH, and CFI.
Adding a 4th column gives 81 possible lines; with 5 columns, there are
243 possible lines. The number of possible left-to-right lines is
always Lines = Rows^Columns.
Ken
···
--- In vpFREE@yahoogroups.com, "Bob Dancer" <bob.dancer@c...> wrote:
My response: I still think my number, which is 6^4 is correct. Label the
squares in the first two positions as
A D
B E
C F
In case the columns don't line up for you on email, I have A B C in the
first column and D E F in the second.
There are six ways to have lines go from first column to the second,
namely:
1. AD, BE, CF
2. AD, BF, CE
3. AE, BD, BF
4. AE, BF, CD
5. AF, BD, CE
6. AF, BE, CD
Each of these six ways may be matched up with the six ways to go from
column 2 to 3 --- and six ways to go from 3 to 4 --- and six ways to go
from 4 to 5. So I think it is 6 * 6 * 6 * 6 = 1,296
[Non-text portions of this message have been removed]