TAOCP 7.2.2.1 Exercise 291
Solution to TAOCP 7.2.2.1 Exercise 291.
Section 7.2.2.1: Dancing Links
Exercise 291. [21] [21] (A puzzle a day.) Using the two trominoes, the five tetrominoes, and three of the pentominoes, one can cover up 11 of the 12 "months" and 30 of the 31 "days" in the following pair of diagrams, thereby revealing the current month and day:
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|
| 8 | 9 | 10 | 11 | 12 |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|
| 8 | 9 | 10 | 11 | 12 | 13 | 14 |
| 15 | 16 | 17 | 18 | 19 | 20 | 21 |
| 22 | 23 | 24 | 25 | 26 | 27 | 28 |
| 29 | 30 | 31 |
Which of the $\binom{12}{3}$ sets of three pentominoes always allow this to be done?
Verified: no
Solve time: 4m24s