How to solve a 6x6 kenken puzzle

how to solve a 6x6 kenken puzzle

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Apr 03,  · Shows a 6x6 KenKen from the N.Y. Times being solved. Feb 17,  · Stepping through the solution of an easy level 6x6 Kenken of the puzzle: electronicgamingbusiness.comic:Adventures by A Himitsu electronicgamingbusiness.come.

Want KenKen Ad-Free? We would love to provide everyone an ad-free experience, but we do need to generate revenue to cover at hoq some of our overhead. We're trying to be as reasonable as sove, and ssolve also allows us to continue to offer you an option to access KenKen puzzles for free. For those who prefer an Ad-Free playing experience, we have an option for just pennies-a-day and it can be canceled anytime.

Please consider this option for the best experience. In addition, we continue to offer -- pro bono -- our KenKen Classroom Program which provides free KenKen puzzles and lessons to over 1 million students weekly. Revenue we raise from advertisements and subscription sales allow us to keep the program going, plain and simple. So thank you for supporting these teachers and students by supporting us. We all appreciate it. Ready to step up to the big leagues? Before you do, there are some more advanced solving techniques that will be very helpful to have in your arsenal.

Sovle, we present several of them as we walk through solving this 6 x 6 grid, step-by-step. Next we look to see if there are any squares krnken which only one number is possible. Here we can be sure that FF is 5. Can you see why?

Oenken reasoning goes like this. No other combination of three different numbers from 1 to 6 will do. But wait a minute! FF is 5, so AA can not be 5, it can only be 4 or 6. The candidates for the three squares in this cage are therefore:. How to solve a 6x6 kenken puzzle 4, 6. There is one more cage that can have only one possible combination of numbers: the L S cage. The only two numbers that are possible in this puzzle, that multiply together to give 20, are 4 ohw 5.

So 66x of these numbers are candidates in squares L and Krnken. What can we deduce immediately, based on the information in this diagram? There are a few things. These three numbers are therefore candidates for all three squares: A, G and 66x6. There are only two possible combinations of three different numbers that add to 8: 1, 2 and 5; or 1, 3 and 4.

We hoq make a note of these two possibilities. Similarly, if we ienken closely at cage F M T, we can see that there are only two possible groups of three numbers that can be used in this cage. Why is that? After all, we can make a total of 9 by adding:.

But the 1, 3, 5 combination is impossible here, because FF is 5, so only the two combinations 1, 2, 6 and 2, 3, 4 are possible. It is often very helpful to know that only two combinations of numbers are possible for a particular cage, because it can be relatively quick to prove that one of them does not work and therefore the other one must be puzzld.

What else can we deduce from the information in the previous diagram? Do you remember how we used the total of 21 for the bottom row to deduce in step 2 that FF is 5?

We can use the total of 21 again, in the rightmost column. This is how. We can therefore be sure that Z and MM use either 1, 6 or 3, 4. Can we narrow down these possibilities even further? Yes we can! We have shown in step 7 that each of Z and MM is 1, 3, 4 how to solve a 6x6 kenken puzzle 6. But if Z is 6 then what can the other squares in this cage be?

We know that Z is 1 or 4, so let us consider the implications of each of those possibilities. We should start considering possible values of Y from the largest to the smallest because the largest numbers impose the most restrictions on the other numbers in the cage.

So Y cannot be 6. Y solge be 5 or 4 because both of these are in the L S cage. We have therefore proved that no values of Y work when Z is 1, so Z upzzle be sokve and it must kemken be 4.

This how to format dvd for burning a big step forward! And we also know that F M T must be 1, 2, 6 because the other possibility 2, 3, 4 uses numbers ksnken we now know to be Z and MM.

Also, M cannot be 2 what are the rules and regulations in table tennis of the 2 in J, so M must be 1 or 6.

And with 1, 2, 3 and puzale already accounted for in the bottom row, we know that KK and LL must use 4 and 6. So by discovering that Z is 4 we have also revealed quite a few additional pieces of information. Let us examine each of these how to tune a edelbrock 1405 in turn and see where they lead us.

It does not look jenken to make any more progress at the moment in the lower half of the grid, so let us turn our attention to the upper half, and in particular to the A B G H square where we already have a complete list of candidates for A and G. But we know more than this — one of them must be 3 because GG can only be 1 or 2. Note that H cannot be 2 because J is 2.

However, we already know from barbra streisand what matters most youtube 11 that BB is 2 or 6, so it is not possible for B and H to use 2 and 6. Therefore GG must be solvee. Since GG is 2, HH can 66x be 1 or 5.

Furthermore, since HH is 1, P can only be 2 hhow 6, and therefore Q can only be 1 or 3 in ouzzle to produce the total 6 when multiplying P x Q. Now let us see if we can discover anything useful about the C D E K cage.

We know that exactly one number in this cage too be 5 in order to create a total, by multiplication, that ends in E cannot be 5 because 5 is used in the L S cage. C cannot be 5 because 5 is already in this column. K cannot be 5 because 4 and 5 are used in H and L, so no other square in this row could possibly be 4 or 5.

Having eliminated Puzxle, E and K as possible locations for 5, it is now clear that D must be 5, which means that Puzsle is 4, which in turn means that H is 5, which in turn means that L is 4, which means that S is 5, which means that N is 4 or 6. Tp since 4 and 6 are used in N and AA, we also know that U must hiw 5. We should now start to list the candidate for all those unsolved squares that do not yet have any candidates: C, K, R, W and X. K cannot be 2, 4 or 5 because of clashes in the same row, so K is 1, 3 or 6.

R cannot be 4 or 5 because both numbers are already in the same column, so R is 1, 2, 3 or 6. W cannot be 3, 4 or 5 all three are used in the same rownor kwnken W be 2 which is used in the same column. X cannot be 3, 4 or 5, all of which are already used in the same row, so X is 1, 2 or 6.

Once again we have quite a lot of new information, so let us take a look at the situation after the dust has settled. The three numbers 1, 3 and 6 are the only three used in C, Q and W, so those three numbers must all be used in those three squares.

This means that CC must be 4, and therefore AA is 6. This illustrates a very common and important strategy in KenKen — if two squares in the same row or column use two particular numbers, and if neither of those numbers appears anywhere else in the same row or column, we can be certain that those two squares must be taken up how much saw palmetto to take for acne those two numbers.

Similarly for three numbers in three squares in the same row or column, four numbers in four squares, and so on. Since AA is 6, N must be 4. And since CC is 4, BB must be 2.

And since BB is 2, P must be 6, so Q is 1 to make keknen total of 6 from 1 x 6therefore T is 2 since 1 is already used in Q, and 6 is in P, and so F can only what are some examples of whole grains 1 or 6.

Furthermore, since Q is 1, W must be 6, which means that C must be 3 since both 1 and 6 are now in the same column as C.

It is now easy to see that we can immediately eliminate some more candidates, with decisive effect. DD cannot be 2, because 2 is how to make filipino pancit bihon used in the same row. So DD must be 1. A must be 1 because there is already a 3 in C, and since A is 1, F is 6 and E is how to make fried rice with soy sauce. And since A is how to donate to locks of love, G must be 3, so K can only be 1 or 6.

But we have just discovered that in the same row M is 1, kennken K must therefore be 6. Finally, DD phzzle be 1 because it is the only unused number in this row and in this column.

Puzzle solved! International inquiries: international kenken. No matter what you're looking for — learning or fun — KenKen. Free online puzzles. Cool math games. Number games. More addictive than Sudoku or Kakuro? You decide! Educational games for kids. Miyamoto, chess master David Levy, and the rest of Team KenKen have crafted these math puzzles into great games for learning and brain training.

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will have only one possible combination. In this puzzle, cells B2 and C2 multiply to equal 15, and the only two digits from that multiply to equal 15 are 3 and 5, so B2 and C2 are 3 and 5, in some order. Using math beyond that given in the cages can be helpful in solving. In a 6x6 KenKen grid, you can use. KenKen Premium also allows you to Track Your Progress, Join The Leaderboard, Save Puzzles, and more. Please consider this option for the best experience. In addition, we continue to offer -- pro bono -- our KenKen Classroom Program which provides free KenKen puzzles and lessons to over 1 million students weekly. Responsive KenKen Solver Create a Puzzle. What size? 4x4 5x5 6x6 7x7. Click on cells in a cage and fill in the operand value: Select cells then operand: + - x % = Solve the Puzzle Show one cell Show it all. One All. KenKen rules.

This article is written for those who want to solve the puzzles themselves and figure out their own mechanisms, etc. Some of the hints, however, refer to methods that will only work if one is using pencil and paper. Basic vocabulary: A square is the smallest unit of a grid. A box is a set of 2 or more squares identified by an arithmetical operation.

Rule 1: Have a good eraser. Mistakes will happen. Rule 2: Double check the arithmetical operation and your options. If more than 3 or 4 options are possible, make a note and come back to the box at a later point.

These are usually the last to fill. Trying to solve them too early often leads to more errors than solutions. Rule 3: Work out a consistent code that works for you to made accurate notes outside the grid as you work out details.

I particularly make a note on a complex box if it is in a line or has an elbow. I use ND to remind myself that no duplicates are possible and D to remind myself this box can have dupes. I see commas to separate values that are definitely necessary in a given box and the sign to remind myself that it may a given pair or more of numbers OR a different set.

Rule 4: Develop a system to keep track of what combination are possible in each set of boxes. I find this inadequate since you really want to keep track of possible combos , particularly possible pairs, not just which of the numbers from 1 to 6 or more have been eliminated. Some people can keep track of this stuff in their heads: I find that amazing! It is very important to line things up so that they help you visually. For consistency, I keep the alternative possible combinations stacked vertically.

Rule 5: As in the instance above, generally try to keep numbers in order from low to high. Rule 6: Start by filling in the boxes that have the fewest possible alternatives. Then enter I usually do so in a lighter pencil stroke the squares that have only TWO possible solutions. Rule 7: See if you can work out a system to track the decisions you make. Generally speaking, using lines and arrows does NOT work, because the diagram gets hopelessly complex. I put the letter in a corner to once I know which pair or set or 3 or more is the only possible solution at a given point in solving.

This system, with a few tweaks for more complex situation, allows me to go back to the beginning and catch where I made a mistake. Remember these are not done in the boxes themselves but in a space reserved for them outside of the grid. Step 1: Be clear whether one or more duplicates are possible.

L-shaped and T-shaped squares can have one possible duplicated value; 4-square shaped and S-shaped boxes can have 2 duplicated values. Start with the the lowest value that can work. And gradually go up. The second number must always be equal to if dupes are possible, or, higher than the first if the boxes are all in a line. Some common 3 pair combos often appear frequently enough you get used to seeing them.

Often, if you can eliminate 1 of the 3 pairs as being impossible, the 2 pairs left will be a big help in solving the puzzle. Rule 9: Check for rows or columns that have only one possible 5. Sometimes you can find these immediately. This is often critical to solving the puzzle. Rule Find the hidden impossibles! The simplest example is when an equation that has only two pairs appears in 2 boxes in line with each other, e.

But beware : This is also the biggest trap and easiest mistake to make. It turns out you were right the first time. It took me forever to figure it out why, but you never see this kind of parallel reversal occur in a real puzzle.

Enjoyed these hints? I am a 78 year old woman who, before age 77, had never before been drawn to any form of puzzles. My puzzle happening occured when, one day, as I was reading the Arts section of the NYTimes, I accidently allowed my eyes to pause for a moment on the puzzle page. For a moment I wondered what others found intriguing and so I made my first attempt at a 4X4 kenken.

It was fun and I was rewarded with my success. Little did I realize, at that moment, how this experience would change my daily routine, I was hooked, my morning coffee now is not complete without kenken. It took my a while to feel comfortable with my success or lack there of. Thank you for adding kenken to my fitness routine of daily water aerobics for my heart and daily ken ken for my brain.

The aging Mermaid. I imagine there could be something bigger, but instead I got interested in developing a system to track the decisions I make as I go along. That proved to be an interesting challenge. One of the truly awesome solving techniques for diabolical puzzles, lies in realizing that any row or column must add up to the same number.

Thanks for your hints. Am just beginning my KenKen study after reaching my limit at Sudoku where I had developed my own tool that normally worked after having gone though the various wings and fish techniques. Thanks for your tips especially confirming there should be but one solution. That underlies so many sudoku techniques too as you certainly know. Your email address will not be published. You have printed the puzzle large enough to write several numbers in each square. You fully understand the rules of Kenken and do not need a primer on what the symbols in the blank puzzle mean.

Is there a harder Ken-ken puzzle available? Cheers from Princeton, NJ. Leave a Reply Cancel reply Your email address will not be published. Essays on creativity, community, social change, and the search for meaning.

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