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Solutions for Act III Scene 3 - Snowdial

The highlighting indicates the importance of triples in this puzzle. Judging by the spread of initial numbers, one could guess that the goal of the puzzle is to fill out the grid, one cell at a time. A reasonable mechanic is by completing triples whenever two out of three numbers are known. The darker cells, on the other hand, seem to contain larger numbers, possibly the sums of the some smaller cells.

So there must be a rule governing the triples. The numbers (19, 57, 98) suggest we should separate the two digits in each number. In particular, (1, 5, 7) and (7, 8, 9) are sets of arithmetic progressions. Now, a rule purely based on arithmetic progressions is not uniquely defined, e.g. when given 3 and 5, the missing number could be 1, or 4, or 7. It also makes sense to have a rule which preserves symmetry between the three numbers. In other words, when given any two out of a triple, the third one can be uniquely determined.

Looking at the cells in the top region surrounding the 318, upon trial and error, we notice that even though there are numerous way of filling them out using arithmetic progressions, only one of them will give 318 when the six surrounding cells are summed. That confirms those six numbers.

Now, we have quite a few confirmed triples so far: (1, 2, 3), (4, 5, 6), (7, 8, 9), (1, 4, 7), (2, 5, 6), (3, 6, 9) and (1, 5, 9). The leap here is to realise that each triple of digits actually forms a straight line when typed on a number pad. The title further confirms this. So the remaining possible triple not used so far would be (3, 5, 7). Using this we can start to fill out more numbers.

When encountering two identical digits in a triple, the sensible thing is to use the same digit for the missing entry. With this we can fill out a significant portion of the snowdial.

At this point, it is not possible to proceed in the same manner on the light cells without trial and error, but we do have three sums in the darker cells. The obvious extension here is to apply the same number pad rule, but on the darker cells. E.g. the darker cell beneath 339 and 316 should be 323. This new information allows us to back solve for the missing summand, then continue as before. The whole board can now be completed. Analogously, the centre cell should be the sum of the six nearest darker cells.

Finally, the three cells indicated by snowflakes contain the numbers 11, 1940, 11. This looks like a date, and indeed it is. A simple search shows the Armistice Day Blizzard started on 11 November 1940. Of course this isn't the only event on that date, but it is the fitting answer. As the Hatter said, “the snowdial will tell you what time it is by the snow!”

The answer is: armisticedayblizzard