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Working With “Either Or” Clues In Logic Puzzles

A lot of logic puzzles contain either / or clues where one set of facts is contingent on another. For example, if you look at clue six in the Game Of Risk puzzle pictured below you will see that it says “of the green player and the person with the most armies, one is Maria and the other dominated North America”.
Now, there are a number of bits of information stored in clues like these. To start with, the “either or” clues are SEPARATE events. So we understand straightaway that the green player did NOT have the most armies, and Maria did NOT dominate the North America part of the board, so we can places Xs accordingly in these squares. These have been circled in blue in the image below.
Once you’ve done this, you can see if we are able to solve the riddle of this clue and unlock the true answers. It is telling us that the green player is EITHER Maria OR North America. From the clues we have so far we are none the wiser as to which of these statements is true. However, the clue is also telling us that the person with the most armies is also EITHER Maria OR North America. Now if we look at the grid we can see that North America actually had 70 armies (circled in yellow) and NOT the most, therefore North America cannot equal the most armies. If North America cannot equal the most armies then it must equal green and we can fill North America and Green as a true answer (circled in yellow). Now we know that it also follows that Maria had the most armies and we can fill that square in as a true answer as well.
In summary – “Either Or” clues can give us a lot of information straightaway but sometimes their secrets have to be unlocked by filling in more of the grid so we can see which of the “Either Or” statements are true or false.

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Watch For Double Negatives In Your Logic Puzzles

A common mistake in solving logic puzzles is simply looking for single true or false answers. Sometimes groups of wrong answers or empty squares can lead you to a deduction. In the example below we are showing how a double negative can lead you to an answer but this can also apply to triple negatives.


In the Prison Sentence example highlighted here we can see that the person at San Quentin either got 15 years or Life. If we look to the right we can see that the person convicted of Theft did NOT get 15 years or Life, therefore could NOT have been at San Quentin. We can therefore mark San Quentin and Thief as an X.

Sometimes we get blinkered looking for single true or false answers and can sit there thinking a puzzle is unsolveable. It could be something as simple as a double or triple negative that could unlock the next stage. Good luck!

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Cross Matching Answers In Logic Puzzles

In the previous posts, we’ve been talking a lot about how you can match pieces of information from one section of the grid to another. To further expand on this, we can use a thing called cross matching when it comes to true answers. In order to explain this, take a look at the grid below:


We can see along the top line that Handel and Tenor are true. If we look down the left side of the grid we can also see that Tenor and 1st are true. This then leads us onto the realization that Handel and 1st must be true because the horizontal and vertical lines of true answers must intersect. If we now know that the vertical colum for 1st is Handel, Tenor, Drew – we then know that the horizontal row for Handel must have the same values . . so 1st, Drew, Tenor.

Following the fact that the true answers must intersect, we then know we can fill in Tenor and Drew as a true answer as well . .  loads of true answers filled in simply by intersecting the lines created by two truths.

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Patterns That Feed Off A True Answer

You can greatly speed up your solving of logic puzzles if you can “see” the patterns on the grid as they start to form. Everything in a logic grid has to slot together so if there are Xs for particular events horizontally then they will need to follow vertically as well.

For example, in the image below we can see that Baritone and 2nd are true. If we look along the grid both horizontally and vertically, you can see various patterns that will match when there is a true answer linking them. In this example, when we look to the right from the Baritone and 2nd true answer, we see that there are Xs showing that the Baritone was NOT Drew or Taylor. These Xs then need to be added to the grid at the bottom because, of course, if Baritone can’t be Drew or Taylor then it follows that 2nd can’t be Drew or Taylor either.

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Looking at this same example, there are several other cells that can be filled in by looking at the other true answers and seeing what information we know about them. For example, we can see that Alto and 4th are true. If we look down from this we can see that Robin was not 4th, so it naturally follows that we can put an X next to Alto and Robin.

Similarly, we know that Vivaldi and Taylor are true, and looking along that line we can see that Vivaldi is not a Soprano or a Tenor, therefore it follows that Taylor can’t be a Soprano or Tenor either. After you have been solving logic puzzles for a while, you will be able to spot the patterns and the way they link together based on true answers.

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