Finishing a Logic Grid Puzzle

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

All six clues have been read, and the grid still has plenty of empty squares. This is normal. The rest comes from four moves, used over and over.

The grid after one pass through the clues.

Move 1: find the last empty square

Look down the 4th column in the top-right grid. $260, $270, $280 and $290 are all crossed out, so the 4th lot sold for $250.

Four X's in the 4th column leave only $250.

A new circle brings new X's, and they often finish another row or column. This one crossed out $250 for the 3rd lot, which leaves the 3rd column with a single empty square: the 3rd lot sold for $290.

The top-left grid has one too. Along the $260 row, Harry, Joel, Kelly and Marco are all crossed out, so the $260 butterfly went to Wallace.

The 3rd column is down to $290, and the $260 row is down to Wallace.

Move 2: carry X's across

The 4th lot sold for $250, so "the 4th lot" and "the $250 butterfly" are two names for the same butterfly. Anything ruled out for one is ruled out for the other.

In the bottom-left grid, the 4th lot has X's against Joel, Kelly and Marco. So the $250 butterfly didn't go to any of them either. Joel's X is already in the $250 row. Add Kelly's and Marco's.

The 4th lot is the $250 butterfly, so the 4th lot's X's belong in the $250 row too.

That leaves the $250 row with one empty square, so Harry won the $250 butterfly.

Carrying X's across has set up another last empty square.

Move 3: reread the clues

Three clues were waiting for more information, and now they have it.

Clue 1 said the 3rd lot was either Joel's or the $250 butterfly. The 3rd lot sold for $290, not $250, so Joel won it.

Clue 4 said the 4th lot sold for $10 less than the 6th lot. The 4th lot sold for $250, so the 6th lot sold for $260. That leaves $270 for the 2nd lot.

Clue 1 gives the 3rd lot to Joel. Clue 4 prices the 6th lot, and the 2nd lot takes the price that is left.

Clue 3 said that of the $260 butterfly and the 4th lot, one went to Harry and the other to Wallace. The $260 butterfly went to Wallace, so the 4th lot went to Harry.

Wallace has the $260 butterfly, so Harry has the 4th lot.

Move 4: carry a match across

The 3rd lot has two circles: it sold for $290, and Joel won it. So Joel's butterfly sold for $290, which is a circle in the top-left grid.

The 3rd lot is $290 and the 3rd lot is Joel's, so Joel's butterfly sold for $290.

Whenever one item has a circle in two grids, the two things it is matched with also match each other.

Now look at the $270 row. Harry, Joel and Wallace are crossed out, and so is Marco, by the false clue from the very start. Kelly is the only one left, and that leaves the $280 butterfly for Marco.

The X from clue 5 decides it: Kelly paid $270 and Marco paid $280.

The last three circles are all carried across. The 6th lot sold for $260 and so did Wallace's butterfly, so Wallace won the 6th lot. In the same way Marco won the 9th lot, and Kelly won the 2nd.

Every row and column of every grid has its circle, and the puzzle is solved.

The answer

Prices	Winners	Orders
$250	Harry	4th
$260	Wallace	6th
$270	Kelly	2nd
$280	Marco	9th
$290	Joel	3rd

If you are stuck

When none of the four moves finds anything, go back through the clues one at a time. An either/or, greater-than or pair clue that gave you little the first time will often give you more once the grid has filled in around it.

If that doesn't help either, the puzzle may need one of the techniques in the second half of this guide, starting with a second look at either/or and pair clues.

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

Next: A second look at either/or and pair clues
Previous: All-different clues
All parts of the guide