Arbor Day Planting

Each of four men who live in Willowbrook Estates on the city’s north side, planted a different type of tree in their front yard on Arbor Day. From The clues, determine the first and last name of each man and the type of tree each planted.

1. George, Mr.Clary, and Mr. Becker (who got his tree from HomeTown Garden Center) all live within three blocks of one another.

2. Mr. Clary planted neither the cedar tree or the maple tree.

3. Harvey and Mr. Clary live next door to one another.

4. The ash tree was not planted by neither John nor Ivan.

5. The maple tree was not the tree planted by George (who is not surnamed Delgado).

6. Mr. Erichsen isn’t the man who planted the ash tree.

7. John, who purchased his tree at the Green Thumb Greenhouse, isn’t the man who planted the sycamore.

Before we start, our ABC grid looks like this:

In Clue 1, we find that three different men are mentioned - George, Mr. Clary, and Mr. Becker, so an “X” goes in the intersection of George and Clary and another “X” in the intersection of George and Becker. These “x’s” indicated we have ruled out these as possibilities.

In Clue 5 we see that George did not plant the maple tree and is not surnamed Delgado, so an “X” goes in the intersection of George and maple, and an “X” at the intersection of George and Delgado.

From Clues 1 and 5, we see that George is not Mr. Clary, Mr. Becker, or Mr. Delgado, so he is Mr. Erichsen, and we can place a “dot” at the intersection of George and Erichsen meaning “Yes”, we have made a deduction. Be sure then to put an “X” at the intersections of Erichsen and Harvey, Ivan, and John to indicate they are not Mr. Erichsen.

Now we can go through the remained of the clues. Clue 2 says Mr. Clary planted neither the cedar or the maple, so “X’s” go in the intersections of Clary and Cedar and Clary and Maple. In Clue 4 we see that neither John nor Ivan planted the ash tree, so an “X” goes in the intersection of John and Ash and Ivan and Ash. Clue 6 says Mr. Erichsen didn’t plant the ash tree, so an “X” goes at the intersection of Erichsen and Ash. And in Clue 7, we find that John didn’t plant the sycamore tree, so we put an “X” in the intersection of John and Sycamore. Now our ABC grid looks like this.

Thus far, this is what we have gotten from the 7 Clues, and at first glance there doesn’t seem to be enough information to make any more deductions, but the information is there. One just has to reread the clues and see what else can be determined.

We know that George is surnamed Erichsen, and George didn’t plant the maple tree [Clue 5] and Mr. Erichsen didn’t plant the ash tree [Clue 6], so an “X” can be put at the intersections of George and Ash, and at Erichsen and Maple. Now we can make another deduction by looking at the ABC grid and that is that the ash tree was planted by Harvey, so we can put a “dot” at the intersection of Harvey and Ash, and “X’s” at the intersections of Harvey and Cedar, Maple, and Sycamore. We also see that Harvey is not Mr. Clary [Clue 3] so an “X” can go in the intersection of Clary and Ash. So by looking under Clary, we see that Mr. Clary planted the sycamore tree, so we put a “dot” for Yes at the intersection of Clary and Sycamore, and “X’s” at the intersections of Sycamore and Becker, Delgado, and Erichsen. We an continue in this fashion by elimination just by looking at the chart.

At this point we have almost all the chart filled in, but there are a couple of extra deductions that need to be made, and that is which of Harvey and John are Becker and Delgado, and since we know that Harvey planted the ash tree and the maple tree, once we determine each man’s surname, the puzzle is finished. But, how do we do that? In Clue 1 it says that Mr. Becker got his tree from the HomeTown Garden Center, and in Clue 7, John got his tree at the Green Thumb Greenhouse, so John is not Becker; he is Delgado and Harvey is Becker. Ta Da! We fill in that information and our puzzle is done, and our ABC grid will look like this:

And the final summary is:

George Erichsen, cedar tree
Harvey Becker, ash tree
Ivan Clary, sycamore tree
John Delgado, maple tree

As mentioned above, there are two ways to solve a logic problem. One is with the ABC crosshatch grid, and another with a table, or fill-in grid. The following example can be better solved with the table or fill-in grid.

Window Flower Boxes

Mary and three other women had flower boxes in windows on either side of their front doors and each woman planted a different type of flower in her window flower boxes (one woman planted petunias). From the clues, can you determine the first name and last name (one is Gumble) of each woman and the type of flower each woman planted?

1. The four women - Julie, Ms. Drake, Ms. Evans, and the woman who planted daisies, all belong to the same gardening club.

2. The woman who planted violets in her flower boxes isn’t Kate.

3. Ms. Drake isn’t the woman who planted marigolds.

4. Ms. Florez, who didn’t plant violets, is married to Lola’s brother.

5. Marigolds were not the flower of choice for Julie.

6. Kate, whose surname isn’t Evans, didn’t plant daisies in her window flower boxes.

If we tried to use an ABC grid, we’d get this far and no further.

However, by using the table or fill-in grid, we will be able to complete solve the problem. Here is what our table looks like:

Now our next step is to start filling in the blanks with our information, and Clue 1 gives us information on all four women, so we will start with that.

First you will notice that in this example, some of the names aren’t mentioned in the clues, so are included in the introduction - first name Mary, last name Gumble, and type of flower, petunia. In Clue 3 we see that Ms. Drake didn’t plant marigolds, and in Clue 5 Julie didn’t plant marigolds, so it was Ms. Evans who planted the marigolds.

In Clue 6, Kate is neither Ms. Evans nor the woman who planted daisies, so she can only be Ms. Drake. In Clue 2, we see that Kate Drake didn’t plant violets, so by elimination, she planted petunias, and it was Julie who planted the violets.

At this point our graph looks like the one above. We can finish it off rather quickly, however. In Clue 4 we see that Julie, who planted violets, isn’t Ms. Florez, so she is Ms. Gumble [mentioned in the introduction], and by elimination, the woman who planted the daisies is Ms. Florez.

Finally, in Clue 4, Ms. Florez isn’t Lola, so she is Ms. Florez is Mary and this leaves Ms. Evans as Lola. Voile! We are done! :-)

And this is our final table or fill-in grid, with the answers. So, as you an see, some logic problems are easily solved with the ABC, or crosshatch grid, while others tend to be solved easier by using the table or fill-in type grid.

• Remember to read the entire logic problem carefully, all the way through, before beginning. Sometimes a clue may be included in the title (although this is rare) or the introduction.

• Read the last sentence or sentences carefully. Know what it is for sure that the logic problem is asking for. For example, does it ask “From the clues, can you determine the first name and last name of each woman and the type of flower each woman planted?” Or does it simply say “What type of flower did Julie plant?” In the latter case, one needs to complete the entire problem in order to made sure that they reach the correct answer.

• If you get stuck, reread the introduction to see if any information is given there that you missed. Then read each clue again, one at a time, to make sure you have gotten all the information that can be extracted from each one.

• Still stuck? Sometimes if one puts the puzzle aside for a few hours, a day, or even a week, then go back to it with a clear mind and you’ll probably see things you missed the first time. This happens more often with longer, more difficult problems.

• In addition, with some puzzles, it may be necessary to develop a tentative hypothesis in order to solve the puzzle. For example, you may be working a problem that wants you to determine the order in which five best sellers were checked out on a Monday morning from the local library, the first and last name of each borrower, and the genre of each book. For example, you have solved the problem to the part where you know that the book, Under The Sun, is either the romance novel or the spy novel, but from the clues you cannot make a determination of which is which. First take the hypothesis that the book is the romance novel and work from there, and continue as if this hypothesis is true. While working, you might find along the way that the third book was checked out by Jack Splat, but from another clue, you have determined that Jack’s surname is Conners, which is a contradiction. Thus, you then know that the book Under the Sun is the spy novel.

• Keep a piece of paper nearby for making tentative hypothesis deductions. In addition, the logic problem you are working may be accompanied by an ABC or crosshatch type grid and one might find that by writing the results of the clues down in table or fill-in grid type form helps to organize your thoughts better. In most logic problem magazines today, both types of grids are provided with the problem, but not always.

• One more thing to try if you are stuck and need a hint is to go to the detailed solution at the back of the magazine. Read through it, one line at a time, until you reach a deduction you didn’t think of. Then stop reading, go back to the logic problem and continue. Most generally you can finish it after that.

Every magazine that deals exclusively with logic problems comes with a page or two in the beginning of solving hints, just as I have given you. However, crossword magazines which have only a few logic problems do not. In addition, most schools require students to be able to solve logic problems of this type for one class or another. I know those who take Chemistry are required to work this type of logic problem, and I am aware that most do not hand out pages on how to solve a logic problem. Therefore, I hope these hints will help you.

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