Let's have a double 6x6 Latin Square (see Figure 1). You can see that this Latin Square has thirteen combinations (see Figure 2). Can you make a double Latin Square that contains the maximum number of combinations and another with a minimum number of combinations? Only numbers from 1 to 6 are allowed.
$\begingroup$
$\endgroup$
11
asked Jan 2 at 22:14
-
$\begingroup$ To be clear, your example in Figure 1 contains 13 pairs (all but 2,6 and 3,5)? $\endgroup$– RobPrattJan 2 at 22:41
-
$\begingroup$ Is 1,2 and 2,1 two different combinations or is that considered the same combination? $\endgroup$– AmorydaiJan 2 at 23:24
-
$\begingroup$ 1,2 and 2,1 is one combination. $\endgroup$– Vassilis ParassidisJan 2 at 23:27
-
$\begingroup$ Where does 2,6 appear in your example? $\endgroup$– RobPrattJan 2 at 23:29
-
$\begingroup$ My example is for demonstration purposes. It is up to you to find the maximum number of combinations. $\endgroup$– Vassilis ParassidisJan 2 at 23:34
|
Show 6 more comments
1 Answer
$\begingroup$
$\endgroup$
1
Minimal:
3 distinct unordered pairs:
16 25 34 43 52 61 25 34 43 52 61 16 34 43 52 61 16 25 43 52 61 16 25 34 52 61 16 25 34 43 61 16 25 34 43 52
Maximal:
21 distinct unordered pairs (which is all of them):
11 22 33 44 55 66 23 34 45 56 61 12 35 46 51 62 13 24 52 63 14 25 36 41 44 55 66 11 22 33 66 11 22 33 44 55
