# How do I reduce a negative hint with multiple possibilities?

This is a hypothetical question about grid-style logic puzzles. I know that when there are positive clues, you reduce the puzzle by eliminating possibilities that don't come in pairs; for example, if the clue is "The one who likes rain plays the flute", you remove all flutes that don't line up in the same columns with rain and all the rain that doesn't line up with a flute. But what about negative clues, such as "Ryan doesn't eat steak" with multiple possibilities for each? If either Ryan or steak is already known, I can eliminate the other from the column they have in common. But I don't know how to treat a clue with multiple possibilities for "not"! How can I glean useful guidance from such a confusing hint?

Here's an example of what I'm talking about:

• I've actually played this specific mobile game. There is nothing to be done until you know the sax or the basketball. But there are many hints, so the expectation is you'll skip to the next hint and utilize this one when it becomes relevant after the sax or ball locations are revealed. Aug 4 '17 at 19:07
• what game is that? Aug 4 '17 at 19:17
• I think I just found it in the Play Store. "Einstein's Riddle Logic Puzzle" Aug 4 '17 at 20:04

The more conclusive way to solve these puzzles is using a grid with more possible interactions - not only the interactions with, say: name and hat; and name and drink; but also hat and drink. Try a grid like this:

What you call a "positive clue" say "The coffee drinker likes dogs" would be incorporated by ticking the box that intersects "Coffee" and "Dogs", and crossing out all the other possibilities like "Coffee" and "Cats", "Horses", ...

A negative clue like "The coffee drinker does not like dogs" would be incorporated by crossing this box.

Then things can start to interact - if there are all but one crosses in a row/column, the remaining one must be the answer. - if the British has White ticked, and White has Tea ticked, then you can tick White and Tea, and all other in those rows and columns can be crossed.

This method has everything the other method has, and more.

• That may be, but I'm seeking to solve the puzzle using only the tools the app has given me. You seem to be recommending that I discard this app and look for a different one; is that what you're suggesting? Oct 22 '17 at 0:13
• I'm unfamiliar with the app that you are talking about. I was talking about how to solve one of these puzzles in general. I'm not really suggesting anything - To be honest when I do the above method to these puzzles it completely takes the fun out of it, because then you aren't figuring anything out yourself, you are just marking ticks and crosses on a piece of paper, and it works out the solution for you. As far as I know this is an exhaustive algorithm that will always give you the answer with no thought. Oct 22 '17 at 0:42
• There are definitely puzzles where simple application of this type of grid doesn't "give you the answer with no thought" - it helps, but additional reasoning is needed. Oct 30 '19 at 20:00

One method I use is something I learned from Sudoku. If there is a pair of the same 2 items in two different boxes, you can eliminate those two items from all other boxes in that line. It even works for trios and quartets, even if all 3 or 4 boxes don't have all of the items. As long as all the boxes don't have anything else. For a trio, it might look like this: ABCDEFGH, AB, AC, ABC, ABCEF, ABCGH You can reduce down to DEFGH, AB, AC, ABC, EF, GH.

• What kind of grid are you referring to here? The rectangular type shown in the question or the stair-shaped type shown in the first answer? Jan 6 at 19:10

Actually the solutions are pretty straight forward.

1) You want to set one row fix. To choose one count the number of green leads (Filter positive + row) and choose the one with the highest amount. In case of tie do the same for negative hints. Form the experience this row is mostly in the lower area.

2) You can fully eliminate all hints for the row from 1). Keep the filter on this row and eliminate all hints until it says no lead left, filter resets automatically at this point.

3) Keep eliminating leads for all rows now just as you did in 2)

4) synchronize green leads. The Highlights in the grid must be in both rows of one Column. Die example you can reduce

GGGX XGGG

to

XGGX XGGX

5) Repeat 3 and 4 whenever possible. Look out for Icons which can be only in one Column left and have an eye for passively fixed icons since the don't remove the Icon passively from other Column. Keep it clean.

6) In most Cases repeating 3-5 already leads you to the solution. If not , then not much is left. I don't why but I went very well by guessing the Icon with the least obvious impact. For example you have

XRRX RRRX

then I guess

XRRX RXXX

Especially if several hints would lead to this same guess. Obviously repeat 3-5 after.