Smythe Dakota wrote:Either way, I don't see how the 4-box can be regarded as a "full jigsaw" -- at least, not if you require that there be nine total pieces, each with nine cells, and that no two pieces overlap.

In the 4-box case, you could, for example, add three "pieces" by considering rows 1, 5, 9 to each be a "piece", but what do you do with what's left? For example, if you wanted to make a "piece" out of r2c1, r3c1, r4c1, r2c5, r3c5, r4c5, r2c9, r3c9, r4c9, you would be changing the original puzzle, because there would be a new requirement that each digit 1 through 9 appear in this "piece".

I guess I might as well explain to Smythe why from logical deduction there must be 5 more disconnected "jigsaw pieces" on the 4-box configuration...

r234c123456789 contain 3 whole rows, thus these 27 cells must have 3 instances of 1 to 9 each.

r234c234 and r234c678 are both defined as "boxes" i.e. they must each contain 1 instance of 1 to 9 each.

Therefore (obviously), r234c159 must have the remaining (3rd) set of 1 to 9 each...

Similarly, r678c159, r159c234 and r159c678 are other 3 implicit "jigsaw pieces"...

Finally, since we have 4 3x3 boxes (r234c234, r234c678, r678c234, r678c678) and 4 implicit jigsaw pieces (r234c159, r678c159, r159c234, r159c678), the remaining 9 cells (r159c159) must contain the remaining (9th) set of 1 to 9 each, thus forming our 9th hidden "jigsaw piece"...

Here is the grid, with each "jigsaw piece" represented by a different letter...

- Code: Select all
`igggihhhi`

eAAAeBBBe

eAAAeBBBe

eAAAeBBBe

igggihhhi

fCCCfDDDf

fCCCfDDDf

fCCCfDDDf

igggihhhi