A Second Look at Either/Or and Pair Clues

Going further, part 1 of 5 of How to Solve Logic Grid Puzzles.

Either/or clues and pair clues each leave two possibilities open. Often you can't tell which one is true, but the grid shows that something is impossible in both. Then it is impossible, whichever way the clue turns out. Puzzle Baron calls this a transitive relationship.

The examples come from Buy Low, Sell High, another puzzle from the app. It has five stocks, five clients, and share prices from $25 to $29. Here it is part-way through.

Buy Low, Sell High after a first pass through its clues.

Either/or: what both options rule out

Clue 6. QMZ was either the stock that sold for $26 per share or the stock Charlie bought.

Could Edith have bought QMZ? Try each option in turn.

If QMZ is the $26 stock: the grid already has an X where $26 meets Edith, so Edith didn't buy it.
If QMZ is the stock Charlie bought: then Charlie bought it, and Edith didn't.

Either way, Edith didn't buy QMZ.

Edith is ruled out for the $26 stock, and she isn't Charlie, so she is ruled out for QMZ.

The pattern to look for: take the other items in the same category as one option (here, the other clients besides Charlie). If the grid rules one of them out for the other option (here, the $26 stock), it is ruled out for the item the clue is about.

Pair clues: swap in what you know

Clue 3. Of the stock that sold for $28 per share and the stock that sold for $27 per share, one was GXTV and the other was bought by Edith.

This clue mixes a stock (GXTV) with a client (Edith), which makes it hard to use. But another clue says who bought GXTV:

Clue 4. GXTV was bought by Geraldo.

So swap Geraldo in for GXTV. The clue now reads: of the $28 stock and the $27 stock, one was bought by Geraldo and the other was bought by Edith.

Both halves are clients now, and the "nothing else fits" step from pair clues applies. The $27 and $28 stocks went to Geraldo and Edith, so nobody else bought them. Cross out Bill, Charlie and Ida Mae for both prices.

With Geraldo swapped in for GXTV, the $27 and $28 rows can only hold Geraldo or Edith.

That is seven X's from two clues that looked used up, and the rest of this puzzle falls to the ordinary moves.

The same idea on a pair clue

"What both options rule out" works on pair clues as well. In a clue such as "Of the 2001 trip and the camping trip, one was with Samuel and the other was with Victor", Samuel went on either the 2001 trip or the camping trip. If the grid shows that the 2001 trip wasn't the kayaking trip, then Samuel didn't go kayaking: the 2001 trip is ruled out by the grid, and the camping trip is a different activity.

Next: Combining greater-than clues
Previous: Finishing the grid
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