Post
by **dickoon** » Sun 02 Sep, 2012 12:53 am

Are we having a thread this year with walkthroughs to the various puzzles? If so, please accept the following as my contribution for one of the few puzzles that I could crack, and a particularly interesting example of the genre; thanks to the constructor, Serkan Yürekli. If my explanation is too quick, please shout up and I'll work through it a bit more slowly. Typoes excepted.

#19 DOUBLE BLOCK (20 pts)

First, work out how many digits must be used to make up each row or column.

Rows first: 9 is 2-3 digits, 6 is 2-3 digits, 11 is 3-4 digits, 2 is 1 digit, 2 is 1 digit, 11 is 3-4 digits, 3 is 1-2 digits.

Columns: 15 is 5 digits, 5 is 1-2 digits, 11 is 3-4 digits, 8 is 2-3 digits, 10 is 3-4 digits.

As 15 is 5 digits, mark R1C2 and R7C2 as blackened and mark R2C2 to R6C2 as numbers.

As R1C2 is blackened and R1 is a 9 which requires 2-3 digits, mark R1C1 as a number, R1C3 and R1C4 as numbers, leave R1C5 and R1C6 blank and mark R1C7 as a number.

As R7C2 is blackened and R7 is a 3 which requires 1-2 digits, mark R7C1 as a number, R7C3 as numbers, leave R7C4 and R7C5 blank and mark R7C6 and R7C7 as numbers.

(Tricky step!) As C7 is a 10 which requires 3-4 digits but R1C7 and R7C7 are numbers, blacken R2C7 and R6C7 and mark R3C7, R4C7 and R5C7 as numbers.

As R2C7 is blackened and R2 is a 6 which requires 2-3 digits, mark R2C5 and R2C6 as numbers, leave R2C3 and R2C4 blank and mark R2C1 as a number.

As R6C7 is blackened and R6 is a 11 which requires 3-4 digits, mark R6C4, R6C5 and R6C6 as numbers, leave R6C2 and R6C3 blank and mark R6C1 as a number.

Observe that R6C2 is a number and R6 has all five numbers marked, so blacken R6C3.

As R3 is a 11 which requires 3-4 digits and R3C7 is a number, mark R3C3 and R3C4 as numbers. As R3C2 is a number, blacken R3C1.

As C5 is a 11 which requires 3-4 digits, mark R4C5 as a number.

As C6 is a 8 which requires 2-3 digits, and because R6C6 and R7C6 are numbers, mark R3C6 as a number.

Observe that R3 has all five numbers marked, so blacken R3C5.

As C5 is a 11 which requires 3-4 digits and R3C5 is blackened, mark R5C5 as a number and blacken R7C5.

Observe that C5 has all two blackened squares marked, so mark R1C5 as a number.

Observe that R1 has all five numbers marked, so blacken R1C6.

Observe that R7 has all two blackened squares marked, so mark R7C4 as a number.

As C4 is a 5 which requires 1-2 digits, blacken R2C4.

Observe that R2 has all two blackened squares marked, so mark R2C3 as a number.

Observe that R4 and R5 are both 2s which require 1 digit each, so one must have C1 and C3 blackened and the other must have C4 and C6 blackened. As C6 is an 8 which requires 2-3 digits, there is not yet an obvious way to tell which is which, so no more numbers can be marked at this point.

Obverve that all rows or columns marked 11 are made up from 3 digits, so they must have 1 and 3 outside the blackened squares and 2, 4 or 5 inside the blackened squares.

Mark R3C6, R3C7, R6C1, R6C2, R1C5 and R2C5 as being "13".

Observe that R2 is a 6 made up of two digits, one of which is either a 1 or a 3. As 33 is impossible, mark R2C5 as a 1 and R2C6 as a 5. Also mark R1C5 as a 3.

(Probably the trickiest step!) Consider C6. As it is a 8 and contains a digit 5 followed by either a 1 or a 3, it is either made up of a 53 or a 512. However, if it is made up of a 512, R4 is impossible, as R4 is a 2, which requires the 2 to be between the two blackened squares. So mark R3C6 as a 3, mark R3C7 as a 1, blacken R4C6, blacken R4C4, mark R4C1 and R4C3 as numbers, blacken R5C1 and R5C3, then mark R5C4 and R5C6 as numbers.

As R4 and R5 are 2s, mark squares R4C5 and R5C2 as 2s as the only numbers between blackened squares in their rows. All squares are now marked as either numbered or blackened.

Observe that C5 now has a 1, 2 and 3 placed. Mark R5C5 and R6C5 as being "45".

Observe that R7 has two numbers marked between the blackened squares. Mark R7C3 and R7C4 as being "12".

Observe that C6 has a 3 and a 5 marked, and R7 has two squares marked "12". Mark R7C6 as 4.

Observe that C6 has a 3, 4 and 5 marked, and R6 has two squares marked "13". Mark R6C6 as 2 and R5C6 as 1.

Observe that C4 has one number marked between the blackened squares and is the column is a 5. Mark R3C4 as 5. This leaves 2 and 4 unmarked in R3, but as R5C2 is 2, mark R3C2 as 4 and R3C3 as 2.

Observe that R6 has a 2 marked and two squares marked "13". As R3C4 is a 5, mark R6 as 4 and R6C5 as 5. As C5 now has a 1, 2, 3 and 5 marked, mark R5C5 as 4.

Observe that R5 has a 1, 2 and 4 marked. As C5 contains a 5, mark R5C4 as a 3 and R5C6 as a 5.

Observe that C7 is a 10, R3C7 is a 1 and R5C7 is a 5. Mark R4C7 as a 4. C7 is now missing a 2 and a 3. As R1 has a 3, mark R1C7 as 2 and R7C7 as 3.

Observe that R7 has a 3 and a 4 marked and two squares marked "12". Mark R7C1 as 5. As R3C3 is a 2, R7C3 is a 1 and R7C4 is a 2.

Observe that C4 has a 5, 4, 3 and 2 marked. Mark R1C4 as 1. As R1 is a 9, mark R1C3 as 5 and R1C1 as 4.

Observe that C3 has a 1, 2 and 5 marked. As R4 has a 4, mark R2C3 as 4 and R4C3 as 3.

Observe that R2 has a 1, 4 and 5 marked. As C2 has a 2, mark R2C1 as 2 and R2C2 as 3.

Observe that R6 still has two squares marked "13". As R2C2 is a 3, mark R6C1 as 3 and R6C2 as 1.

Only R4C1 and R4C2 are open; as C1 is missing a 1 and C2 is missing a 5, mark R4C1 as 1 and R4C2 as 5.

Finished; read off marked rows for answer.