Egghead Games

Greater Than and Less Than Clues in Logic Grid Puzzles

Part 3 of 6 of How to Solve Logic Grid Puzzles.

Some categories have a natural order: prices, times, ages, months. A clue can compare two items using that order, with words like more, less, before or after.

Clue 4. The insect that was auctioned 4th sold for 10 dollars less than the insect that was auctioned 6th.

Read this one slowly, because the puzzle has two kinds of number. "4th" and "6th" say when a butterfly came up in the auction. The clue compares what those two butterflies sold for: the 4th lot's price was $10 below the 6th lot's price. Prices go up in steps of $10, so the 4th lot is one step below the 6th lot.

Trim the ends

Suppose the 4th lot had sold for $290. The 6th lot would then have sold for $300, and there is no such price. So the 4th lot didn't sell for $290. In the same way, the 6th lot can't have sold for $250, because nothing sold for $10 less.

Butterfly Streamline Illustration: https://streamlinehq.com $250$260$270$280$2902nd3rd4th6th9thHarryJoelKellyMarcoWallace2nd3rd4th6th9thWINNERSORDERSPRICESORDERS
The cheaper lot can't have the top price, and the more expensive lot can't have the bottom price.

The size of the gap sets how many squares to cross out. With a gap of two steps, cross out two prices at each end. A plain "less than" with no amount works like a gap of one.

Use what the grid already says

From clue 2, the $280 butterfly was the 9th lot, so neither of these two lots sold for $280. Those X's are already on the grid, and each one rules out a price for the other lot:

An X for one lot becomes an X for the other, one step away.

The 4th lot is now down to $250 or $260, and the 6th lot to $260 or $270.

A clue with an exact gap is worth rereading every time you learn something about either item. This one comes back in the last part.

When the items are in different categories

Clue 4 compares two lots, which are both in the orders category. A clue can also compare items from different categories, such as "Kelly's butterfly sold for less than the 9th lot".

That kind holds a hidden false fact. Kelly's butterfly sold for less than the 9th lot, so it can't be the 9th lot. Put an X where Kelly meets 9th, then trim the ends as usual.

Practise on puzzles like these in our Logic Grid Puzzles app, for iPhone, iPad, Android and Amazon Fire.

Next: Pair clues
Previous: Either/or clues
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