| devjoe ( @ 2009-06-23 21:45:00 |
| Entry tags: | wpc |
USPC Post-Mortem
Having looked over the puzzles I didn't solve during the competition, and having solved most of them, I really think I made some bad choices in puzzle selection, some of them ones I should have known better about. I don't know if anybody else will benefit from this, but hopefully I read this before next year's USPC and make better choices because of it.
In numerical order:
13. C Notes
Well duh, add up the current values of each row or column, and see that none of the rows are correct mod 10, nor are any two the same mod 10. The only way to change the mod 10 sum is to add a digit after one of the numbers, and doing so makes the same change in a mod 10 sum of the corresponding row and column. So not only do I need an after-digit in each column, but I need at least four total after-digits arranged so that two of them are in the same row and the other two are in the same column (the only way to avoid having one row and one column with only a single after-digit between them), or I need five after-digits (two in the first row, one in the second, and two in the last row are the most possible).
Since the middle row cannot take two after-digits, and the first row cannot take two after-digits on the 7 and 5, and (for four-after-digit cases) the last row can only take two after-digits on the last two numbers because otherwise you'd have two numbers in a column adding to more than 100, there are only three ways to place four after-digits, and each one has a row or column that determines (by mod 10 sum) what the digit has to be. Furthermore, there is one cell in a row and a column with all four of the after-digits, and it needs to work (possibly with a before-digit) to make both of those lines add to 100 at the same time. These cases can all be checked quickly this way to see that they don't work.
So we must have five after-digits, 2-1-2 by rows, and some permutation of 2,1,2 in the columns, where the 1s are not allowed to coincide in the same cell. This can be searched as: Choose one cell in the middle row to get the after-digit, and solve for it. Now choose another cell in that cell's column to get an after-digit, and solve for it and the required before-digit for the other cell in this column. Choose another cell in the second after-digit-cell's row, and solve for its required after-digit. In the remaining row, the two after-digits go in the columns that don't already have two after-digits; solve for them. This row is now completely filled, and must add to 100. Due to the same restrictions as in the four-after-digit cases, some of these cases can be immediately ruled out, and there are just 6 more cases to check.
I'm not sure I can work through all this logic fast enough to be worth the 10-point solve, but it works out that there are only *9* cases to check the math on, when initially it just looks like hundreds.
14. Lucky Sevens
There's no way I should have skipped this. Try pairs of words as the first words in 7x7 blocks that could go in either the upper left or lower right. Find that there are exactly two possible blocks. One of them cannot go on the upper block because it has wrong letters as the starts of words for the other blocks, so place one block in the grid, and after solving a couple other words, place the other block (it can be flipped across the diagonal).
19. Magic Puzzle'Rs
In competition, I found the three forced entries through the given P, U, and C, and saw that one of the names starting with R had to go vertically through the given S. Then I missed the next step and skipped it. But duh, MERRELL has two Rs, and by the magic R rule, can only go into this grid on the diagonal. One of the two places he could go blocks all ways of using the S, so put him in the other, and the rest solves rather quickly.
If I had devoted the time I spent not-solving the Yajilin on solving these puzzles, I should have had 50 more points, breaking 200, which is a score I wouldn't feel so bad about.