Aug 20 hard solving guide
P/p as in this puzzle is poop in my opinion. It somehow made the hard ones earlier in the week seem like a walk in the park. I just got absolutely stumped trying to come up with a strategy to attack this puzzle. Below is the mess of a walkthrough I came up with (bear in mind I tried to avoid pip counting at all costs, which may be the easier solution?). Would be very interested to know how others solved this (other than trial and error). Would also be curious to know how the former guide master would have attacked this (if he didn't hold a grudge against us all).
- >!There are five doubles (0-0, 3-3, 4-4, 5-5 and 6-6). By forced placement, each of the three 3c= must contain one.!<
- >!The only whole domino with a sum of 3 is the 1-2.!<
- >!Very few tiles can fit in the bottom of the 3c9. The 6-6, 6-5, 6-4 and 5-5 are all too large, and the 0-0 and 0-1 are too small. The 6-3 and 5-4 would need to be followed by a 0-x (with x>4), which doesn't exist. The 4-4 would need to be followed by a 1-x (with x>4) which doesn't exist. The 2-5 would need to be followed by a 2-x (with x>4) which doesn't exist. This leaves three possibilities: 3-3 (finished with 3-6), 3-4 (finished with 2-5), or 1-2 (finished by either 6-6 or 6-5).!<
- >!Note that in all of these combinations (3-3-3, 3-4-2 or 1-2-6), the 3c9 is composed of two numbers ≤3.!<
- >!There are 11 total "small tiles;" three 0s, two 1s, two 2s and four 3s. The 2c<3 requires two. Each 2c3 require two. Two go into the 3c9. Three remain.!<
- >!The only possible places that can take a number ≤3 are the 1c>0, discard, 3c= or [one more in the] 3c9.!<
- >!Let's assume for a moment that the 3c= takes a low number. The only ones with enough are 0s or 3s.!<
- >!If the 3c= is 0s, all 0s are booked, which means that both 2c3s are 1+2, and now all numbers ≤2 are booked and we can't complete the 2c<3.!<
- >!If the 3c= is 3s, there's one 3 remaining. Which means that the 3c9 can only be 3-4-2 or 1-2-6. Either way, one 2 is booked. This means that one of the 2c3s has to be 0-3, which books the last 3, and forces the 3c9 to be 1-2-6 (with the 1-2 in the bottom). The other 2c3 would have to be 1+2 also. This books all 1s, all 2s and all 3s. So the 2c<3 has to be 0+0. And the 2c<3 can't be made of two tiles (because then the left half of either the 0-0/0-1 goes into the 2c>10, which doesn't work), so it would be the whole 0-0. BUT then this fails, because above this the 2c3 would need a whole domino, and we already used the 1-2.!<
- >!So therefore a 3c= is not made from a number ≤3. So they are made of 4s, 5s and 6s.!<
- >!This also means that the three remaining low numbers have to go into the 1c>0, discard and 3c9.!<
- >!Which means that the 3c9 is made of three low tiles, and this has to be 3-3 with the 3-6 above it. Three 3s are booked, one remains.!<
- >!The 2-5 is now more limited as to where it can go. It can go on the 1c>0-3c= border (on the left in the capital P), the discard-3c= border (on the top of the capital P), or the 2c<3-2c>10 border. No matter where, one 2 is therefore going into a place that is NOT a 2c3. So one 2c3 is a 0+3 (which books the last 3), and one is a 1+2 (which books the other 2). This leaves us with two 0s and one 1 to fill out the remaining unfilled spaces of the 1c>0/discard/2c<3.!<
- >!If the 2-5 goes in either slot within the capital P, it would require the 2-1 to go into the 2c3. But then this would be followed with either a 0/1 going into a 3c=, and since there is none with a half of 4/5/6, this fails.!<
- >!So the 2-5 goes on the 2c<3-2c>10 border in the lowercase p.!<
- >!The 2c<3-2c3 border can be the 0-0 or 0-1. If it's the 0-1, the 2c3 is finished with the 2-1 going into the 3c=, which fails. So it's the 0-0, followed by the 3-4 and then the 4-4.!<
- >!The 0-1 now only has one place to go, it's on the discard/2c3 border in the capital P with the 0 in the discard. This is followed by the 2-1 beneath it into the 1c>0.!<
- >!There are two 4s remaining, and they must go into the two 1c>3 slots. The 4-6 is on the 1c>3-2c>10 border to finish the lowercase p, and the 4-6 is on the 1c>3-3c= in the capital P.!<
- >!Finish this 3c= with the 6-6.!<
- >!The 1c>4-3c= on the right of the capital P is therefore the 5-6, and finished with the 6-6.!<
Q.E.D. I say good riddance to this puzzle.