The Contest Center - SumSum Puzzle

SUMSUM^TM

       SumSum is a new kind of puzzle that uses numbers and logic. SumSum is like a crossword puzzle that uses numbers instead of letters. There is a grid where you can write the numbers. Your job is to figure out which numbers to write in which squares. You do that by using the clues.

       Each puzzle will have some rules telling you what numbers to use. For instance, the rules might say "Write the numbers from 1 to 5." You would write the numbers from 1 to 5 into 5 of the squares in each line. A line can be a row or a column. Rows read across and columns read down.

       That will leave 2 squares over. You can fill in the other 2 squares solid black, like a crossword puzzle. The black squares split each line into several sections called runs. There can be 1, 2 or 3 runs in a line. The two black squares in a line never touch each other, but they may touch the black squares from other lines.

CLUES

       To the left of each row is a wide box with the clues for that row. The clues tell you the sum of the numbers in each run. The clues are given in order, from left to right. In this example the clues are 5, 1 and 9.

       The first run is 2 and 3. The first clue is 5, which is 2+3. The second run has the single number 1, so the second clue is 1. The third run is 5 and 4. The third clue is 9, which is 5+4.

5,1,9

It works the same way in the columns, going from top to bottom.

       Now that you know all about the grid and the clues, you are ready for

SOME SUPER SUMSUM SOLVING SECRETS

       You can be a SumSum genius if you know a few simple tricks. The clues to the left of each row and at the top of each column tell you what numbers to use. For example, if a clue is a 1 or a 2, then you will use a single 1 or a 2 because there is no way for two different numbers to add up to 1 or 2.

       The number of clues tells you which squares must be black and which squares must be white. Some black squares can be placed immediately. If a line has only one clue, then the two end squares must be black. All the rest of the squares must be white.

       This line has only one clue, which is 15. So you know that the two black squares must go at the ends of the line. You can mark them black by filling them in. You can mark squares that must be white with a dash, like this

If a line has three clues, then both end squares must be white. This example has three clues, 5, 6 and 4. So you can mark the two end squares white, like this

5,6,4

If a line has two clues, then one end square must be white and the other end black. If you know that the square at one end is white, then you can mark the other end black. If you know that the square at one end is black, then you can mark the other end white.

The two black squares in any line can't touch. So, every time you mark a square black, you can mark the surrounding squares white, like this

		-			-
1,12,2	1		-	-		2
		-			-

When there are only two squares left in a line that don't have to be white, those last two squares have to be black.

Once you have found where the two black squares go, you can mark all the other squares in that line white, like this

5,8,2

After you have found some of the black squares, start looking for places where there is just a single white square. The clue will tell you what number to put there. In both of these examples, the number in the yellow square has to be 4.

6,4,5

5,5,5

LET'S TRY AN EXAMPLE

Take a look at this line from a SumSum puzzle. This puzzle uses the numbers from 1 to 5.

1,8,6

Since there are 3 clues on this line, the first square must be white. The first clue is 1. The only way that you can make 1 using the numbers 1 to 5 is with the single number 1. This tells you that the first square must contain the number 1, and the second square must be black.

1,8,6

This leaves 5 more spaces. The second clue is 8. It will take at least 2 numbers to add up to 8. You can mark the next two squares white, like this

1,8,6

The third clue is 6. It will also take at least 2 numbers to add up to 6. You can mark the last two squares white, like this

1,8,6

That leaves only one more square. The last square has to be black, like this

1,8,6

You can finish the puzzle by doing the same thing in the other lines.

THE WHOLE THING

Now that you know how to tackle each line, you are ready to try a complete puzzle. Here is a puzzle from the SumSum puzzle website. This puzzle uses the numbers from 1 to 5.

SumSum	10 5	5 4 6	15	3 7 5	2 6 7	8 5 2	3 12
9,6
3,6,6
8,5,2
2,13
9,6
8,4,3
1,14

A good place to start is to mark the squares that have to be white. Remember, if there are 3 clues for a row, then the first and last squares have to be white. If the clue is more than 5, then there have to be at least 2 white squares.
Changes will be highlighted in yellow.

SumSum	10 5	5 4 6	15	3 7 5	2 6 7	8 5 2	3 12
9,6
3,6,6	-					-	-
8,5,2	-	-					-
2,13
9,6
8,4,3	-	-					-
1,14

Whenever a clue is a 1 or a 2 that run can have only one number. You can write that number right away, and you can mark the next square black.

SumSum	10 5	5 4 6	15	3 7 5	2 6 7	8 5 2	3 12
9,6
3,6,6	-					-	-
8,5,2	-	-					2
2,13
9,6
8,4,3	-	-					-
1,14

All of the squares next to a black square must be white.

SumSum	10 5	5 4 6	15	3 7 5	2 6 7	8 5 2	3 12
9,6
3,6,6	-					-	-
8,5,2	-	-			-		2
2,13						-
9,6
8,4,3	-	-					-
1,14

Now let's do the same thing for the columns.

SumSum	10 5	5 4 6	15	3 7 5	2 6 7	8 5 2	3 12
9,6		-		-	2	-
3,6,6	-					-	-
8,5,2	-	-			-		2
2,13						-
9,6
8,4,3	-	-					-
1,14		-		-	-	2

When a line has only 1 clue, both end squares have to be black, and the 5 middle squares must be white. You can mark all of the squares in column 3.

SumSum	10 5	5 4 6	15	3 7 5	2 6 7	8 5 2	3 12
9,6		-		-	2	-
3,6,6	-		-			-	-
8,5,2	-	-	-		-		2
2,13			-			-
9,6			-
8,4,3	-	-	-				-
1,14		-		-	-	2

Look at the top row. The first run totals 9. You need at least 2 numbers to make 9, so the upper left corner must be white. There are 2 clues for the top row, so if the first square is white, the last square must be black. The same for the first column. So the upper right corner and the lower left corner must be black. That means the lower right corner is white. That finishes all 4 corners.

SumSum	10 5	5 4 6	15	3 7 5	2 6 7	8 5 2	3 12
9,6	-	-		-	2	-
3,6,6	-		-			-	-
8,5,2	-	-	-		-		2
2,13			-			-
9,6			-
8,4,3	-	-	-				-
1,14		-		-	-	2	-

Now you can fill in a few of the numbers by sight.

SumSum	10 5	5 4 6	15	3 7 5	2 6 7	8 5 2	3 12
9,6	-	-		-	2	-
3,6,6	-		-			-	1
8,5,2	-	-	-		-		2
2,13			-			-
9,6			-
8,4,3	-	-	-				3
1,14		1		-	-	2	-

That makes it clear where some more of the black and white squares have to be.

SumSum	10 5	5 4 6	15	3 7 5	2 6 7	8 5 2	3 12
9,6	-	-		-	2	-
3,6,6	-		-	-		-	1
8,5,2	-	-	-		-		2
2,13			-			-
9,6			-				-
8,4,3	-	-	-		-		3
1,14		1		-	-	2	-

Now there are a few more single numbers that can be filled in by sight.

SumSum	10 5	5 4 6	15	3 7 5	2 6 7	8 5 2	3 12
9,6	-	5		-	2	-
3,6,6	3		-	-		5	1
8,5,2	-	-	-		5		2
2,13			-			-
9,6			-				-
8,4,3	-	-	-		4		3
1,14		1		5	-	2	-

Row 4 has just 2 clues. Since the last square is black the first square must be white. Row 5 is exactly the opposite.

SumSum	10 5	5 4 6	15	3 7 5	2 6 7	8 5 2	3 12
9,6	-	5		-	2	-
3,6,6	3		-	-		5	1
8,5,2	-	-	-		5		2
2,13	-		-			-
9,6			-				-
8,4,3	-	-	-		4		3
1,14		1		5	-	2	-

In column 4 and column 6 both of the black squares have been marked. All the other squares in those columns must be white.

SumSum	10 5	5 4 6	15	3 7 5	2 6 7	8 5 2	3 12
9,6	-	5		-	2	-
3,6,6	3		-	-		5	1
8,5,2	-	-	-		5		2
2,13	-		-	-		-
9,6			-	-		-	-
8,4,3	-	-	-		4		3
1,14		1		5	-	2	-

Now more of the missing numbers can be filled in.

SumSum	10 5	5 4 6	15	3 7 5	2 6 7	8 5 2	3 12
9,6	4	5		1	2	3
3,6,6	3		4	2		5	1
8,5,2	-	-	-		5		2
2,13	2		-	-		-
9,6			-	-		-	-
8,4,3	5	-	-		4		3
1,14		1		5	-	2	-

On row 6 the 2 missing numbers must be either 1,2 or 2,1. But there is already a 1 in column 2. That means the 2 missing numbers must be 2,1 in that order.

SumSum	10 5	5 4 6	15	3 7 5	2 6 7	8 5 2	3 12
9,6	4	5		1	2	3
3,6,6	3		4	2		5	1
8,5,2	-	-	-		5		2
2,13	2		-	-		-
9,6			-	-		-	-
8,4,3	5	2	1		4		3
1,14		1		5	-	2	-

That lets you fill in the rest of column 1 and column 2. There is only one place left for the last black square, so you can mark that, too.

SumSum	10 5	5 4 6	15	3 7 5	2 6 7	8 5 2	3 12
9,6	4	5		1	2	3
3,6,6	3		4	2		5	1
8,5,2	1	4	-		5		2
2,13	2		-	-		-
9,6		3	-	-		-	-
8,4,3	5	2	1		4		3
1,14		1		5	-	2	-

You can now finish row 3 and column 5.

SumSum	10 5	5 4 6	15	3 7 5	2 6 7	8 5 2	3 12
9,6	4	5		1	2	3
3,6,6	3		4	2		5	1
8,5,2	1	4	3		5		2
2,13	2		-	-	1	-
9,6		3	-	-		-	-
8,4,3	5	2	1		4		3
1,14		1		5	3	2	-

You can now finish row 7. That will let you fill in some more numbers.

SumSum	10 5	5 4 6	15	3 7 5	2 6 7	8 5 2	3 12
9,6	4	5		1	2	3
3,6,6	3		4	2		5	1
8,5,2	1	4	3		5		2
2,13	2		-	-	1	4
9,6		3	-	-		1	5
8,4,3	5	2	1		4		3
1,14		1		5	3	2	4

The last 2 numbers on row 4 can only be 3,5 or 5,3. Since there is already a 3 in column 3, the only choice is 5,3. That gives you the last 2 numbers, and the puzzle is finished.

SumSum	10 5	5 4 6	15	3 7 5	2 6 7	8 5 2	3 12
9,6	4	5		1	2	3
3,6,6	3		4	2		5	1
8,5,2	1	4	3		5		2
2,13	2		5	3	1	4
9,6		3	2	4		1	5
8,4,3	5	2	1		4		3
1,14		1		5	3	2	4