999_Springs wrote:knowing that all 7x7 pandiagonal solution grids are cyclic makes the puzzle (and perhaps all 7x7 pandiagonals) very easy

Yes, that's an easy way to solve it. You could say the same of all the 11x11 grids. Which leads to the conclusion that only 13x13s and above are "interesting". Unfortunately, they are much too large for being really interesting for many manual solvers.

All the 7x7s I've seen are quite easy. It'd be interesting to look for the hardest possible ones (not using cyclicity in the solution).*

This puzzle remains easy even if one doesn't know or want to use cyclicity (basically, one Naked-Pairs):

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`Resolution state after Singles (there are no Singles):`

3 1 2457 45 6 457 25

4 56 356 1357 2 1357 1567

1256 7 1245 3456 1345 1456 235

125 2345 1356 124567 457 23567 134567

157 345 1234567 1256 57 234567 123456

1567 3456 12457 23567 135 12456 23457

2567 2456 3567 123457 1345 1235 14567

As in many Pandiags, there are lots of whips[1] at the start (I usually skip this part in my Sudoku answers, but people are not yet used to whips[1] in Pandiags):

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`whip[1]: c5n4{r7 .} ==> r7c2 ≠ 4`

whip[1]: c2n4{r6 .} ==> r5c3 ≠ 4

whip[1]: c2n2{r7 .} ==> r7c6 ≠ 2, r4c6 ≠ 2

whip[1]: c6n2{r6 .} ==> r5c7 ≠ 2, r6c7 ≠ 2

whip[1]: a2n2{r7c1 .} ==> r3c1 ≠ 2, r5c3 ≠ 2, r7c4 ≠ 2

whip[1]: a6n2{r6c4 .} ==> r4c4 ≠ 2

whip[1]: c4n2{r6 .} ==> r6c3 ≠ 2

whip[1]: d1n7{r6c3 .} ==> r6c7 ≠ 7

whip[1]: d4n6{r5c7 .} ==> r5c6 ≠ 6

whip[1]: r5n6{c7 .} ==> r2c7 ≠ 6

whip[1]: r2n6{c3 .} ==> r6c6 ≠ 6

whip[1]: a1n6{r7c7 .} ==> r4c7 ≠ 6

whip[1]: c7n6{r7 .} ==> r6c1 ≠ 6, r7c2 ≠ 6

whip[1]: c2n6{r6 .} ==> r4c4 ≠ 6

whip[1]: r4n6{c6 .} ==> r7c3 ≠ 6

whip[1]: r7n6{c7 .} ==> r3c4 ≠ 6

whip[1]: c4n6{r6 .} ==> r5c3 ≠ 6

whip[1]: c5n7{r5 .} ==> r5c6 ≠ 7, r4c4 ≠ 7, r4c6 ≠ 7

whip[1]: r4n7{c7 .} ==> r2c7 ≠ 7

whip[1]: c7n7{r7 .} ==> r7c3 ≠ 7, r7c4 ≠ 7

whip[1]: r7n7{c7 .} ==> r6c1 ≠ 7

whip[1]: r6n7{c4 .} ==> r5c3 ≠ 7

whip[1]: d4n3{r5c7 .} ==> r5c3 ≠ 3

whip[1]: a4n1{r3c6 .} ==> r3c1 ≠ 1

whip[1]: c1n1{r6 .} ==> r5c7 ≠ 1

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`Resolution state after Singles and whips[1]:`

3 1 2457 45 6 457 25

4 56 356 1357 2 1357 15

56 7 1245 345 1345 1456 235

125 2345 1356 145 457 356 13457

157 345 15 1256 57 2345 3456

15 3456 1457 23567 135 1245 345

2567 25 35 1345 1345 135 14567

naked-pairs-in-an-anti-diagonal: a6{d1 d7}{n1 n5} ==> d4a6 ≠ 5, d4a6 ≠ 1, d2a6 ≠ 5, d5a6 ≠ 5, d3a6 ≠ 5, d6a6 ≠ 5

stte

(*) Up to now, the hardest 7x7 seems to be 1to9only's puzzle:

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`. 1 . . . . .`

4 . . . . . .

. . . 3 . . 5

. . . . . . .

. . . 6 . . .

. . . 2 . . .

. . . . . . .

It requires a Naked Triplet (or z-chains[3])