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Judy's Logic Problems
Contructing a Logic Problem - Page 2
STEP #1
After that, when I thought I was ready to do my own, I started out with a simple enough method. I made a table and entered my elements into it with the summarized solution I wanted to end up with it. For example, say I decide to do a logic problem on five couples getting engaged and each man bought his fiance an engagement ring with a different type of stone. Also each couple got engaged in a different month. The table following shows what the conclusion is I want to end up with.
NOTE: You will have your categories, and under each category will be your variables. The number of categories and variables can be different with each puzzle. The one I'm using is considered a 5x4, which means it has 5 variables under 4 categories.
| MAN |
WOMAN |
STONE |
MONTH |
| Abraham |
Olivia |
Sapphire |
August |
| Benjamin |
Maryann |
Emerald |
May |
| Cornelius |
Pauline |
Black Onyx |
June |
| Daniel |
Nanette |
Diamond |
July |
| Edward |
Lillie |
Ruby |
April |
Notice that the names of all the men in the first column down are in alphabetical order, but the others are not. That is because when I finally write out my introduction and ask for a conclusion, and also list my summary at the end of my detailed solution as one sees in magazine publications, this is the way they do it.
It is also mentioned in my guidelines for submissions, which you should also read even though you may not want to submit any to be published here. Those guidelines are also part of constructing a logic problem and are very important. When contacting a publication inquiring as to their needs, they will send you guidelines very similar to those I listed and so one would be way ahead in the game if they are already in the habit of following them.
STEP #2
Okay, now on to the puzzle! After making my table, I use what I call the pairing method to get me started for the first four or five clues. I also use what I refer to as 'color coding' and that is using highlighters or markers of various pastel colors to select the information for each clue. Most quidelines usually state that around six clues is average for an easy to medium puzzle with four categories [MAN, WOMAN, STONE, MONTH], as I have above. However, from viewing logic problems in magazines, one will see that anywhere from five to eight are acceptable.
NOTE: On my example here I use a different colored font instead of background so that if you want to print out the page, it will use less colored ink, and the background of your table/chart will be white.
With the pairing method, one can use a variety of combinations, such as MAN-WOMAN, MAN-STONE, MAN-MONTH, WOMAN-STONE, WOMAN-MONTH, AND STONE-MONTH. In larger puzzles, with more categories and variables, one can do this with even one or two combinations of three, although I'd keep that a minimum.
| MAN |
WOMAN |
STONE |
MONTH |
| Abraham |
Olivia |
Sapphire |
August |
| Benjamin |
Maryann |
Emerald |
May |
| Cornelius |
Pauline |
Black Onyx |
June |
| Daniel |
Nanette |
Diamond |
July |
| Edward |
Lillie |
Ruby |
April |
Okay, now we have the basic information for the first five clues. Also, I added a bit to clues 2 and 5 so that the sentences wouldn't appear so flat and short, and also may come in handy later when adding more clues. Here are the clues I've come up with:
1) Abraham gave his bride-to-be a sapphire ring.
2) It was in May that Maryann received her ring from her High School sweetheart.
3) Pauline received a ring with a beautiful black onyx.
4) Daniel and his girlfriend got engaged in July.
5) Edward and Lillie are planning to honeymoon in Cancun.
STEP #3
Now, we have five clues, but do we know we have five couples? At this point the solver doesn't know this for sure, as it could be that Pauline who got the black onyx is engaged to Daniel, or that Abraham got engaged to Maryanne. We will take Clue 4 first and see what we can do to remedy part of this situation. Lets change that clue to read:
4) Daniel and his girlfriend, who is not Pauline, got engaged in July.
At this point we have determined that there are at least four different couples mentioned in the five clues given. From our 'color coding' and the clues, the constructor knows there are five couples mentioned, but the solver can't know that with the information given. So far we have:
1) Abraham gave his bride-to-be a sapphire ring.
2) It was in May that Maryann received her ring from her High School sweetheart.
3) Pauline received a ring with a beautiful black onyx.
4) Daniel and his girlfriend, who is not Pauline, got engaged in July.
5) Edward and Lillie are planning to honeymoon in Cancun.
Now, clue 2 states that Maryann got engaged in May, but she could have gotten engaged to Abraham. We can remedy this situation just as we did with Clue 4. Here are a couple things we can change:
1st - Abraham, who got engaged in either August or April, gave his bride-to-be a sapphire ring.
And/Or
2nd - It was in May that Maryann received her ring from her High School sweetheart, who is neither Abraham nor Cornelius.
If we change both clues as they stand, basically we are giving the same information about Maryann not being engaged to Abraham twice [Abraham in Aug. or Apr. and Maryann in May says the same as Maryann not receiving ring from either Abraham]. However, a fact need only be mentioned once in a good logic problem. Thus, we can remedy this by simply dropping Abraham out of the 2nd example. We are still changing both clues, but coming to only one conclusion. Now our five clues are:
1) Abraham, who got engaged in either August or April, gave his bride-to-be a sapphire ring.
2) It was in May that Maryann received her ring from her High School sweetheart, who is not Cornelius.
3) Pauline received a ring with a beautiful black onyx.
4) Daniel and his girlfriend, who is not Pauline, got engaged in July.
5) Edward and Lillie are planning to honeymoon in Cancun.
At this point, we still have five clues, but much more information. From the clues we have now, we can now make some deductions: Maryann [May] was not engaged to Abraham [August or April], Daniel [July], Edward [Lillie], or Cornelius [clue 2], so she was engaged to Benjamin. Also we can deduct that Pauline, who got black onyx , didn't get engaged to Daniel [not Pauline in clue 4] or Abraham [sapphire in clue 1], so she got engaged to Cornelius. Therefore, our five clues give information about five couples and the solver now knows some facts about all five couples.
Thus, our chart now looks like this:
| MAN |
WOMAN |
STONE |
MONTH |
| Abraham |
********* |
Sapphire |
Aug or April |
| Benjamin |
Maryann |
********* |
May |
| Cornelius |
Pauline |
Black Onyx |
******** |
| Daniel |
********* |
********* |
July |
| Edward |
Lillie |
********* |
********* |
STEP #4
We are now ready to add another clue or two to finish the puzzle off. Notice how we spruced up the clues with extra phrases, such as in Clue 5 about Edward and Lillie planning to honeymoon in Cancun? Adding the Cancun part can work to our advantage here. Now we might add a clue which says. . . .
6) A diamond sparkles on the ring finger of the left hand of the woman who plans to honeymoon with her new husband at Lake Tahoe in either June or July. Olivia and her intended plan to honeymoon at Niagra Falls.
Okay, this tells us then that it was not Edward who gave Lillie the diamond since they plan to honeymoon in Cancun and not at Lake Tahoe, nor is it Benjamin and Maryann since they plan to marry in May, and it can't be Cornelius and Pauline since Pauline got the black onyx, or Abraham and his intended since he gave her a sapphire. . .thus, it can only be Daniel and his bride-to-be. So Daniel gave his bride-to-be a diamond and they plan to marry in July [from Clue 4]. It also states that this woman is not Olivia [Niagra Falls] so it can only be Nanette, which leaves Abraham's intended as Olivia.
Also, we combined two facts in clue 6 - the one about the Lake Tahoe couple and the one about Olivia, and that is perfectly okay as they both have something in common - where they plan to honeymoon.
Now our chart looks like this:
| MAN |
WOMAN |
STONE |
MONTH |
| Abraham |
Olivia |
Sapphire |
Aug or April |
| Benjamin |
Maryann |
********* |
May |
| Cornelius |
Pauline |
Black Onyx |
******** |
| Daniel |
Nanette |
Diamond |
July |
| Edward |
Lillie |
********* |
********* |
STEP #5
We'd like to finish this up with only one more clue if possible. So we can do it simply this way. Remember we paired up Pauline and Cornelius by deduction and elimination. Also, we still don't know which woman received the ruby or which woman received the emerald. Here is what we have so far:
1) Abraham, who got engaged in either August or April, gave his bride-to-be a sapphire ring.
2) It was in May that Maryann received her ring from her High School sweetheart, who is not Cornelius.
3) Pauline received a ring with a beautiful black onyx.
4) Daniel and his girlfriend, who is not Pauline, got engaged in July.
5) Edward and Lillie are planning to honeymoon in Cancun.
6) A diamond sparkles on the ring finger of the left hand of the woman who plans to honeymoon with her new husband at Lake Tahoe in either June or July. Olivia and her intended plan to honeymoon at Niagra Falls.
We can make one final clue simply by saying this:
7) Cornelius plans to marry sometime later in the year than the woman who received the ruby (who was not Maryann), but earlier in the year than at least one other couple.
Okay, this tells us that Cornelius didn't get engaged in either April [earliest month] or August [latest month] according to the chart we made. Nor did he get engaged in July as Daniel did from Clue 4, or in May, as we have determined that Maryann and Benjamin did. Thus, he had to have gotten engaged in June.
It also states that Maryann didn't get the ruby, so the one who got the ruby was Lillie, and it also leaves Lillie as the woman who got engaged in April. That leaves two places to be filled in by elimination - one is that Maryann got the emerald and that Abraham and Olivia were engaged in August.
STEP #6
So now we have completed our clues and we have what we want the final summation to be to our logic problem, except for one thing. While doing the clues, following the pairing method , we simply went down the chart making our clues. However, we want the solver to have to work for the answer - that is the fun of a logic problem. So our last step in making the clues is to change them around a bit. Following will be what we shall use in our final logic problem.
1) A diamond sparkles on the ring finger of the left hand of the woman who plans to honeymoon with her new husband at Lake Tahoe in either June or July. Olivia and her intended plan to honeymoon at Niagra Falls.
2) It was in May that Maryann received her ring from her High School sweetheart, who is not Cornelius.
3) Abraham, who got engaged in either August or April, gave his bride-to-be a sapphire ring.
4) Pauline received a ring with a beautiful black onyx.
5) Daniel and his girlfriend, who is not Pauline, got engaged in July.
6) Cornelius plans to marry sometime later in the year than the woman who received the ruby (who was not Maryann), but earlier in the year than at least one other couple.
7) Edward and Lillie are planning to honeymoon in Cancun.
STEP #7
And now our clues are done. On to the next step, which will be to think of a title and do the introduction.
TITLE
We know there are five women and each received an engagement ring, but in most cases, an engagement ring is a diamond engagement ring. In our puzzle only one woman got a ring with diamonds, so lets try and think of a catchy title dealing with that. Lets go with "Engaging Moments." Why not? :-) It's not the best in the world and can always be changed later if we decide to. Now we have the title, we need to write the introduction.
FACT GATHERING FOR INTRO
Introductions are short scenarios explaining the situation and asking for a conclusion. First off, we want to look at our clues to see what parts of each elements are mentioned in the clues, for those that are not included in the clues need to be mentioned in the introduction. Our clues are:
1) A diamond sparkles on the ring finger of the left hand of the woman who plans to honeymoon with her new husband at Lake Tahoe in either June or July. Olivia and her intended plan to honeymoon at Niagra Falls.
2) It was in May that Maryann received her ring from her High School sweetheart, who is not Cornelius.
3) Abraham, who got engaged in either August or April, gave his bride-to-be a sapphire ring.
4) Pauline received a ring with a beautiful black onyx.
5) Daniel and his girlfriend, who is not Pauline, got engaged in July.
6) Cornelius plans to marry sometime later in the year than the woman who received the ruby (who was not Maryann), but earlier in the year than at least one other couple.
7) Edward and Lillie are planning to honeymoon in Cancun.
First off, four of the five men are mentioned in the clues [Cornelius in 2, Abraham in 3, Daniel in 5, and Edward in 7], but Benjamin is not mentioned, so needs to be included in the introduction. Of the women, four are mentioned in the clues [Olivia in 1, Maryann in 2, Pauline in 4, and Lillie in 7], but Nanette is not mentioned in the clues, so she needs to be included in the introduction.
Of the months, all five are mentioned [June and July in 1, May in 2, and August and April in 3], but in most cases, magazine publication guidelines ask that dates [time, day, month, year, etc.] or numbers be mentioned in the introduction, regardless of whether they are all mentioned in the clues or not. This type of inclusion varies from publication to publication. However, it is a good practice to do so. As for the gems, the diamond is mentioned in clue 1, sapphire in 3, the black onyx in 4, the ruby in 6; thus, the emerald must be mentioned in the introduction. Okay, so lets now write the introduction. We shall make it pretty basic and simple.
INTRODUCTION
Engaging Moments
"Last year, Benjamin and four other men became engaged to be married. Each man gave his girlfriend (one of whom is Nanette) an engagement ring, each of which had a different stone (one contained a fabulous emerald). Each of the five couples became engaged in a different month - April, May, June, July, or August. From the clues, determine the woman to whom each man became engaged, the gem in the ring each man gave his bride-to-be, and the month in which each couple became engaged."
Notice that when asking the question, I put them in order: man, woman, gemstone, and month - just as they appear in my chart and which will appear as titles in the table I make for the puzzle, as well as in the short summary at the end of the detailed solution.
DETAILED SOLUTION & SUMMARY
Each couple got engaged in a different month - April, May, June, July, or Aug. (intro). Daniel got engaged in July (5) and Abraham in either Aug. or Apr. (3), so Maryanne, who got engaged in May (2) didn’t get engaged to Daniel or Abraham, nor did she get engaged to Cornelius (2) or to Edward [engaged to Lillie](7); thus, Maryanne got engaged to Benjamin in May. Cornelius doesn’t didn’t get engaged in either Apr. or Aug. (6), so he is the one who got engaged in June, and it was Abraham and Edward [Lillie] who got engaged in Apr. and Aug., in some order. Benjamin didn’t give Maryanne [May] a diamond [June or July], sapphire (3), or black onyx [Pauline], nor did Maryanne get the ruby ring (6), so she got the emerald ring. Cornelius [June] got engaged later in year than woman who got the ruby (6), so it was woman who got engaged in Apr. who got the ruby [May was Maryanne who got emerald]; thus, the woman who got the ruby in Apr. didn’t get engaged to Abraham [sapphire]; therefore, it was Lillie who got engaged to Edward who got the ruby in Apr., and, by elimination, it was Abraham who gave his girlfriend the sapphire ring in Aug. Daniel didn’t get engaged to Pauline (5) and since Pauline got the black onyx (4), she didn’t get engaged to Abraham [sapphire](3); thus, Pauline got the black onyx ring from Cornelius in June, and, by elimination, Daniel gave his girlfriend the diamond ring. The woman who got the diamond plans to honeymoon at Lake Tahoe, so isn’t Olivia, who plans to honeymoon at Niagra Falls (1), so Daniel [gave diamond] didn’t get engaged to Olivia; he got engaged to Nanette (intro) and it was Abraham who got engaged to Olivia.
In summary:
Abraham, Olivia, sapphire, August
Benjamin, Maryanne, emerald, May
Cornelius, Pauline, black onyx, June
Daniel, Nanette, diamond, July
Edward, Lillie, ruby, April
And we are done! We have our Title, Introduction, Clues, and Detailed solution with the Summary following it. And On the next page we will look at another method of constructing a logic problem. The detailed solution for it will look similar with the clue numbers and deductions in parentheses and brackets, as shown here. Lets take a look at another method for constructing logic problems, one I call the overlap method. So on to page 3! :-)
Logic Problem Page
Construct a Logic Problem - Page 1
Construct a Logic Problem - Page 3
Construct a Logic Problem, Hints & Tips - Page 4
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