Puzzle Network: GC43FX2 - A Blue-Frosted KenKen

GC43FX2 - A Blue-Frosted KenKen

By: sandlanders

1. Here is the puzzle.
In case you haven't run across a "KenKen" puzzle before (it's also called "mathdoku" and "calcudoku"), we've listed some of the directions you might want to know about the puzzle. Once you solve this particular puzzle, you will see numbers in the boxes that have the letters A-F in them in the grid. Replace the corresponding letters in the red coordinates shown below with those numbers. You can then find the cache container, a bison tube, at that winter-friendly location. It's not all that hard... just use a bit of brain power.

Some directions for solving this puzzle and others similar to it:

Fill the whole 7x7 grid, one digit per square.

Use the digits 1-7 so that there is one and only one of each digit in each column and each row.

An outlined box can contain a repeat of a digit as long as they are not in the same row or column.

Within each box, place chosen digits so that they give the indicated number for the box by using the indicated operation. ( + is add; - is subtract; * is multiply; / is divide )

N 44 28.ABC W 089 30.DEF

2. Learn how to solve KenKen puzzles.

Here is a link to an excellent site that will teach you how to solve KenKen puzzles.

Tutorial - KenKen Puzzle Official Site

3. Solve the KenKen Puzzle.

Original Puzzle

Step 1

Start by filling in single boxes that have bold borders. Notice that these boxes do not have a mathematical function. They contain only a small number in the upper left corner. This number is the solution for this single box.

Step 2

According to the rules of the game, since this is a 7x7 grid, the only numbers that can be used are 1-7, and each number is only used one time per row or column. Utilizing the boxes that have solved numbers, look for sets of boxes (in pink) which have solutions that are easy to identify.

For 4*, the only numbers 1-7 that when multiplied together will give 4 as an answer are; (1,4), (2,2). Since 2 can't be in the same column more than once, (1,4) must be used. Since 1 can't be in the same row twice, the 1 goes in the top box and the 4 goes in the bottom box.

For 5*, The only numbers 1-7 that can be multiplied to give 5 as an answer are; (1,5). Since 1 can't be in the same row twice, 1 goes in the top box and 5 goes in the lower box.

Step 3

Now notice that every column and row has a number 1 filled in, except one; the top row, second column. Fill in 1 at that location.

For 3+, only two numbers 1-7 can be added together to get 3 as an answer; (1,2). Since there is already a 1 in the leftmost column, 2 will go in the left box, and 1 will go in the right box.

For 3/, the only digits 1-7 that can be divided to get 3 as the answer are, (6, 2, 1), as follows:
6 / 2 / 1 = 3. Since the 1 can't go in the left column, it will go in the right-hand box. There is no way to tell which boxes the 2 & 6 go into yet, so we will place them in both boxes (in red) to hold those boxes for these digits.

Step 4

For 140*, the only digits 1-7 that can be multiplied together to get 140 are (4, 5, 7). Since the first column already has a 5, the 5 must go in the bottom right box. There is no way to tell which boxes the 4 & 7 go into, so we will place these digits in both boxes, in red, to hold their place in the column.

That leaves only the numbers 2 & 6 to complete the first column, so we will look at 84* next.

For 84*, we already have the digits 2 & 6, so that means the third digit must be 7, which will go in the top right box. Since there is a six in the bottom row, the 6 will go in the top left box, and the 2 will go in the bottom left box.

For 3/, with the grey background; because of the solution for 84* that we just solved, we now know that the 2 must go in the bottom box, and the 6 must go in the top box.

Step 5

For 12*, the only available numbers that will solve this multiplication problem are (3,4). Since the order can't be determined, they will be placed in both boxes, for now. The only other number that remains for this row is 5, which should be placed in the last box on the right.

Step 6

Notice that there are two sets of boxes with 3- in the last column. Because 5 & 1 have already been solved for this column, the only sets of numbers that can be subtracted to get an answer for 3 are, (7,4) and (6,3). Since we don't know which set goes where, we will put all four digits in each box.

The only number that remains for the last column is 2, so it should be placed in the only remaining box that doesn't have a number.

Step 7

For 2-, the only remaining digits for this column that will solve this subtraction problem and give an answer of 2 are (6,4). Since there is already a six on the lower row, 6 goes in the top box and 4 goes in the lower box.

The only remaining number for this row is 3, which should be placed in the bottom box.

Step 8

For 350*, the only numbers needed to complete this row are 5 and 7, and they satisfy the multiplication equation (5 x 2 x 5 x 7 = 350). Having two 5's in the equation is not a problem, because the 5's are in different rows. Since there is no way to tell which box the 5 & 7 belong in, they will be placed in both boxes, for now.

For 2/, the following sets of numbers are available to satisfy this division problem, (6,3), (4,2). The set (2,1) is not available, because both columns have a 1 in them already. Notice that 6 will not work in the left-hand box and 4 will not work in the right-hand box. The possible solutions have been adjusted accordingly.

Step 9

For 126*, the only available numbers that will solve this equation are (7,6,3). The correct order is not known, so these digits will be placed in the boxes where they could possibly be used. Because 7, 6, and 3 are no longer available for use in this column, 2/ and 350* can be solved.

Once the 2/ and 350* equations have been solved, 140* and 12* can also be solved.

Lastly, the grey boxes in the far right column can be modified to reflect their remaining possible solutions.

Step 10

For the column that starts with 2/ only two remaining numbers are needed, 2 & 5. The 5 goes in the top box, because there is already a 2 in the upper of the two rows. The 2 goes in the bottom box, because there is already a 5 in the lower of the two rows.

To complete the 16+ equation, only 6 & 3 will solve the equation. Since there is already a 6 in the lower row, the 6 will be placed in the top left box. The 3 goes in the lower left box.

Now, the far right column can be finished. The only solution that will work for the top set of boxes is (3,6), which means that (4,7) is the solution for the lower set of boxes. Using the solved digits for each of the rows, the correct location for each number can be determined.

Step 11

Rows 2 an 3 only need one number each. Fill in 7 on row 2, and fill in 4 on row 3.

Now look at columns 3 and 4, which only need two numbers each. Row 3 needs the numbers 3 and 5, and row 4 needs the numbers 5 and 7. Using the solved numbers from the relevant rows and columns, fill in the remaining numbers. For column 4, the number 5 goes in the top box and 7 goes in the bottom box. For column 3, the number 3 goes in the top box and 5 goes in the bottom box.