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If you're new to grid-based logic puzzles, this tutorial will teach you the basics. Start with the "Introduction" first, then move on to the tutorials discussing specific clues or solving methods. Each tutorial contains a number of different slides - you can advance to the next slide by clicking "Next slide" at the bottom of each page, or by using the circled numerical links below each slide. Choose your specific tutorial from the list below to get started.
Slide #1
Transitive relationships for unaligned pair clues follow the same logic as those for either/or clues. It's all about finding pre-existing true/false relationships for one item in relation to its partner item's category.
It may be hard to believe, but using nothing but transitive relationships, clue #5 and the existing grid state shown here, no less than fourteen new false relationships can be placed on the grid. Let's find out how...
Slide #2
Look first at the subcolumn for "blue" in relation to prices (shaded in yellow). We know from the existing grid state that blue == $55.
Can you guess how that can be inserted into clue #5 in a transitive relationship?
Slide #3
Since blue == $55, simply replace "blue" in clue #5 with "$55". Now the clue says "Of Zachary and the person who got the Aquarius tattoo, one paid $55 (blue) and the other paid $40."
Therefore, Zachary can only be $40 or $55, and Aquarius can only be $40 or $55. That gives us the first six false eliminations (shaded in green).
Slide #4
Now look at the subrow for $40 in relation to colors (shaded in yellow). Can you find the next transitive relationship with clue #5?
Slide #5
$40 can only be pink or red, so that sets up a new transitive relationship with clue #5.
According to clue #5, Zachary can only be blue or $40 (which can only be pink or red) - therefore Zachary can only be blue, pink or red. The same goes for Aquarius - it can only be blue, pink or red.
This gives us the next four false relationships (shaded in green). Zachary cannot be orange or violet, and Aquarius cannot be orange or violet.
Slide #6
Two more transitive relationships remain to be found. Can you find them?
Hint: look for true or false relationships for Zachary in relation to zodiac signs, or true or false relationships for Aquarius in relation to names.
Slide #7
First transitive relationship: Zachary doesn't equal Taurus (see yellow column) - therefore blue can't equal Taurus and $40 can't equal Taurus.
Second transitive relationship: Aquarius doesn't equal Bonita (see yellow row) - therefore blue can't equal Bonita and $40 can't equal Bonita.
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