Knighty Knight (Quadratum VI by Oyler)
Since The Magpie didn’t do blogs in their pre-electronic era you were spared blogs for QI – QIV. Those of you who are old enough would perhaps have thought that it had something to do with Spike Milligan’s TV programmes though!
This will be mercifully short and builds on the previous one for QV. Hopefully solvers read that blog and AJ’s solution, both of which alluded to, but did not state explicitly that the sum of the four numbers collected would be the same in a block if the starting position of the knight was in any of the four corner cells. A different total can result if it was in one of the four edge cells.
That was the reason why some of the clues for a block just gave the sum of the four numbers collected as that would allow solvers to decide which out of a number of sets was the correct one. Both knights started in the same cell so the end cells and start cells in a block are fixed and for both knights they will be of the same type.
If we take the above block as an example and a knight enters at 1, say, the tens digits of the numbers collected are 1, 3, 5 and 7 and the units digits 2, 4, 6 and 8. This gives a sum for the 2-digit numbers of 180. If it enters at 3 then that total will still be the same. Whereas if it enters at 2 then the sum is 216. In fact, so long as the sum of the corner digits is different from that for the edge digits this will always be the case. If it is the same then the totals will be the same.
In the puzzle, the anti-clockwise knight in block I collected four triangular numbers in ascending order. There are three possible sets: 28, 36, 45, 91; 21, 36, 45, 78 and 36, 45, 78, 91. So, which set to use? Helpfully, the clockwise knight collected four numbers that summed to 200. The sums for the three possible sets are 200, 180 and 250 respectively. The one you needed was the first set.
In a sense I just wanted to see if solvers had taken notice of the previous blog and AJ’s solution and had learnt something!
October 2nd, 2024 at 9:10 pm
I don’t think I remembered anything from your last blog or the solution notes, but solving QV definitely helped make QVI much more approachable. It’s like muscle memory for puzzles. Thanks for explaining your didactic theme!