# Logic grid puzzle

I found some logic puzzles on someone's blog from a few years ago, and have been trying to solve them. Here's the link to the page.

Please let me know if you have any suggestions! I have looked at this from different points of view and tried various methods of solving, but am quite stuck.

Although I sometimes use the provided grid for solving logic puzzles, for this specific puzzle I did not, nor do I think it is necessary. For this one, I used the first clue to create four separate "columns" of information, each one representing one of the four women and all of her various characteristics (instructor name, number of sessions, spa treatment, etc.). Then, I went through all the clues repeatedly, and gradually added information to each of the columns as I could deduce it. I was able to solve the entire puzzle this way.

My first step was the following line of reasoning:

Look at the entire first clue and the second sentence of the clue #2. The four "columns" I made based on the first clue are: 1. Alissa, 2. the kickboxing student (fewer sessions than Alissa), 3. Hans' student, and 4. the woman who got the facial (more sessions than Hans' student). The second sentence of clue #2 tells us that Drake is the instructor teaching 12 sessions. We were told at the start that the four women ordered 12, 13, 14, and 15 sessions. 12 is the smallest of these. Of the four "columns", Drake can only fit in the second one. It can't be column 1, because Alissa has more sessions than the kickboxer (thus, more than 12). It can't be column 3 because Hans is the instructor there, so it can't also be Drake. It can't be column 4 because that woman had more sessions than Hans' student (thus, again, more than 12). So Drake, with 12 sessions, is placed into column 2, and the layout of what we know looks like this:

| Alissa | Drake, 12 sessions, kickboxing | Hans | facial |

My second step was the following line of reasoning:

Clue 5 tells us that the number of lessons booked with Raoul is exactly one fewer than the number of lessons booked with Otto. We already know that Drake is teaching the fewest number of lessons (12), and that Hans is not teaching the most (because, from clue 1, the woman who got the facial booked more sessions than Hans's student. So Hans must be teaching either 13 or 14 sessions. But is cannot be 14, because then that would leave 13 and 15 for Raoul and Otto, but we already know that Raoul is teaching exactly one less than Otto. So we can conclude that Hans must be teaching 13 lessons, and Raoul 14 and Otto 15. Furthermore, clue 5 tells us that neither Raoul nor Otto teaches pilates. So Hans must be the pilates instructor, as we already know that Drake is teaching kickboxing. Now the "columns" look like this:

| Alissa | Drake, 12 sessions, kickboxing | Hans, 13 sessions, pilates | facial |

For the next step:

Look at clue 3. We can worry about the Calvin Klein part later. For now, note that Lisbeth is taking yoga, and purchased fewer training sessions than the woman who got a massage. We already know that the 12 sessions are for kickboxing and the 13 sessions are for pilates, so Lisbeth, who is taking not kickboxing nor pilates, but yoga, must be taking 14 sessions, as we know from clue 3 that someone else is taking more sessions than her. So Lisbeth is either in the first column, or the fourth. She can't be in the first column, as that is Alissa, so Lisbeth must be in the fourth column and must be the one who got a facial. Alissa, then got the massage. That must be the case, as she is the only person who bought more lessons than Lisbeth, and we were told that Lisbeth bought fewer lessons than the person who got the massage. Lisbeth is taking yoga, so Alissa must be taking the only remaining course: spinning. Now we also know where to place Raoul (14 sessions) and Otto (15 sessions) as well, and the columns look like this:

| Alissa, Otto, 15 sessions, spinning, massage |
| Drake, 12 sessions, kickboxing |
| Hans, 13 sessions, pilates |
| Lisbeth, Raoul, 14 sessions, yoga, facial |

For the next step:

Look at the first part of clue 4. We have already placed two of the women by name: Alissa and Lisbeth. The start of clue 4 tells us that Gillian did not pay for 12 sessions. So we can conclude that she must have paid for 13 sessions (the 14 and 15 sessions are Lisbeth and Alissa). That leaves Tiffany with 12 sessions. Our columns now look like this:

| Alissa, Otto, 15 sessions, spinning, massage |
| Tiffany, Drake, 12 sessions, kickboxing |
| Gillian, Hans, 13 sessions, pilates |
| Lisbeth, Raoul, 14 sessions, yoga, facial |

Gillian did not get the pedicure. We already know that Alissa got the massage, and Lisbeth got the facial, so Gillian must have gotten the mud wrap, and Tiffany, then, got the pedicure:

| Alissa, Otto, 15 sessions, spinning, massage |
| Tiffany, Drake, 12 sessions, kickboxing, pedicure |
| Gillian, Hans, 13 sessions, pilates, mud wrap |
| Lisbeth, Raoul, 14 sessions, yoga, facial |

All that is left is determining

the sportswear that each woman bought. First of all, we know from clue 3 that Lisbeth purchased Calvin Klein. That leaves Tommy Hilfiger, DKNY, and Polo (mentioned in the puzzle introduction). We know from clue 4 that Gillian did not purchase Tommy Hilfiger, but we also know something else due to the way this clue is written: we know that the woman who purchased Tommy Hilfiger is a different woman from the woman who had the pedicure. So looking at our columns, we can see that only Alissa could have purchased Tommy Hilfiger. We know from clue 2 that Tiffany didn't purchase DKNY, so Gillian must have. That leaves only Polo, which must have been purchased by Tiffany. And now the columns are complete:

| Alissa, Otto, 15 sessions, spinning, massage, Tommy Hilfiger |
| Tiffany, Drake, 12 sessions, kickboxing, pedicure, Polo |
| Gillian, Hans, 13 sessions, pilates, mud wrap, DKNY |
| Lisbeth, Raoul, 14 sessions, yoga, facial, Calvin Klein |

As you should be able to see, the order in which you consider the clues is very important. In most logic puzzles, the clues are deliberately presented in an order different from the optimal order needed for solving. So rather than consider them in the order given, you should read through them repeatedly, and at each step in solving work with whatever clue will best help you to deduce new information. You should also note that you might use the various parts of a single clue at different times. For example, I used the second part of clue 2 near the beginning, but I didn't use the first part of this clue until near the end.

• Thanks so much for the help! It makes much more sense now! May 1, 2020 at 18:25