by **Guest** » Fri May 06, 2005 8:41 pm

Not to be difficult, but your example is not a valid 2x2

e.g

12

23

is not a valid upper left box.

Number of possibilities:

Upper left (UL) box: 4! = 24

UR box given each UL: 2x2 = 4

Lower Left (LL) box given each UL = 4

LR box given LL,UR = Either 0 or 1

Therefore there are >24*4*4 candidates, or >374.

Sample where LR is unfillable:

12 43

34 12

23 ??

41 ??

where two boxes in LL cannot be filled by any number.

If you look at the 16 possibilities for UL and LR, given each arrrangement of UL (of which there are 24), it turns out that 4 of them result in an unfillable LR. Therefore there are 12 that are good, for a total number of valid answers of 12*24=288.

{That's a MUCH easier puzzle to do than the 3x3.}