This months ClueJo logic problem has to do with archery and in order to solve it, you will need to know a little about the color/point system on the target in order to determine points earned.
Archery is one of the world’s oldest and most popular sport and involves shooting bows and arrows. On the archery range, archery targets are know as butts. Regulation butts are 48-inches in diameter and the target’s gold center, known as the bull’s-eye, has a scoring value of 9 points. Going outward from the bull’s-eye are four rings painted red, blue, black, and white, in that order, and have a point value of 7, 5, 3, and 1, respectively. The remaining surface of the target, known as the apron, is painted green and has no scoring value. The arrow consists of four parts, one of which is the shaftment, which extends from the nock (where the bowstring fits when one is preparing to shoot) to just in front of the feathers (which help guide the arrow). In many cases and archer will use a particular color in the area in front of the feathers on the shaftment as a personal marking for identification.
Although there is much history about archery, for this particular logic problem, the above information is what you will need to solve the following logic problem. Hope you enjoy it!
Mr. Boddy’s land holdings are vast and last year he donated some land to the county to set up an archery range, archery being a hobby of his. Then he got his six friends - Col. Mustard, Miss Scarlet, Mr. Green, Mrs. Peacock, Mrs. White, and Prof. Plum interested in the sport. One day last week he visited the range to find all six out doing target practice. As he chatted, he noticed that each had colored his or her arrow shaftment with a different color - black, blue, gold, green, red, or white (the same colors which make up the butt). At the time of Mr. Boddy’s arrival, each of the six characters had already taken three practice shots and had accumulated a different score. From the information below, determine the color each character had used on his or her shaftment and the points each accumulated. Note. To solve, you will also need to determine the number of points made in each practice shot, although the order in which they were made is not important.
1. None of the archers had so far hit an area on the target which corresponded in color with the color each had chosen for his or her arrow shaftment.
2. Each colored area on the target, including the apron, had been hit more than once.
3. Upon Mr. Boddy’s arrival at the archery range, he found that Miss Scarlet was exactly 3 points ahead of one archer and exactly 3 points behind another.
4. Out of the four bull’s-eyes hit at the time of Mr. Boddy’s arrival, three were made by two different indidviduals - the one who had painted his or shaftment red and the one who had painted his or her shaftment green.
5. Mr. Boddy found that the man whose arrows were marked with black was exactly 2 points ahead of Prof. Plum.
6. Only one archer had thus far hit the same colored area on the butt more than once, but he or she was not the archer who had the highest score totaling 21.
7. As Mr. Boddy chatted with his friends, he discovered that the blue area of the target had been hit more often than the black area, which had been hit more often than the white area.
8. Mr. Green, who uses the color gold on his shaftment, had the lowest score of 8 at the time of Mr. Boddy’s arrival. However, the week previous he had gotten the most points so no one was complaining!
9. The only three characters who had earned 7 points by hitting the red area around the bull’s-eye during one of their practice shots were Col. Mustard, the woman with the blue markings on her shaftments, and the person whose total accumulated score was 15.
10. One of the female characters had thus far, at Mr. Boddy’s arrival, hit the bull’s-eye, the blue area, and the apron during her practice shots. This was not Mrs. Peacock, who uses the color white as a personal marking on her arrows.
Back to Year to Year Logic Problem Page
| SUSPECT | SHAFT COLOR | POINTS I | POINTS II | POINTS III | TOTAL POINTS |
I’ve done a few logic problems where a few people make statesments, and some tell the truth, some lie, and some both tell the truth and lie. Very similar to these are the “Knight & Knave” type logic problem, and I recently came across some I had collected in a folder in my file box. I decided it would be fun to share them with you. I also receive quite a bit of E-mail asking for help on problems of this type, and I simply don't have the time to answer them all, along with questions about my regular logic problems, so hopefully these will help those that need help in that area.
In most of these Knight & Knave problems, they live on an island and a stranger is nearly always involved, but sometimes there is another inhabitant of the island who sometimes lies and sometimes tells the truth. Here, we will refer to that person as a Jester. A Knight always tells the truth, a Knave always lies, and a Jester can both tell the truth and lie. The stranger just goes around asking questions or eavesdropping on conversations. :-)
So lets have a little fun with a few Knight and Knave situations. I’d like to add that I have collected these little gems over several years and have no idea where I got them, but I do know I collected them from several different sources. If I have infringed on anyones' copywrited material, please let me know and I will remove that problem immediately.
A. Three of the inhabitants of an island - A, B, and C - were standing together outside the court house. A stranger passing by stopped and asked A, “Are you a Knight or a Knave?” A mumbled rather indistinctly, so the stranger didn’t catch his answer. The stranger then turned to B and asked, “What did A say?” B replied, “A said that he is a Knave.” At this point, the third man, C, said, “Don’t belive what B said; he is lying!”
The question is, what are A, B and C?
B. Now, what if the conversations had been as follows: Suppose the stranger, instead of asking A what he is, asked A, “How many Knights are among you?” Again A answers by mumbling indistinctly, so the stranger then asks B, “What did A say?” B replies, “A said that there is one Knight among us.” Then C says, “Don’t belive what B said; he is lying!”
Now what are A, B and C?
C. The mysterious stranger comes upon two other inhabitants of the island in a garden, which we will also refer to as A and B. Before the stranger can say one word, A makes the statement, “At least one of us is a Knave.” “Ahhh,” says the stranger. The rumor has spread, so he knows he is expected to come up with an answer to their identity.
What are A and B?
D. The stranger wanders on and comes upon three people, A, B, and C standing in front of a fountain in the park. Again, before the stranger can ask a question, A and B make the following statements: A says, “All of us are Knaves,” and B refutes that by saying, “Exactly one of us is a Knight.”
What are A, B, and C?
E. However, lets see what would happen if A says, “All of us are Knaves, and B refutes this by saying, “No, exactly one of us is a Knave.”
Can it be determined what B is? And what about C?
F. This one is more difficult. Now the stranger comes across two more of the inhabitants of the island, A and B. Before they can say a word, he asks A, “Is either of you a Knight?” After the stranger received an answer from A, he knew the answer to his question.
What are A and B?
G. Now lets throw in a Jester. As mentioned in the introduction to this section, a Jester is someone who sometimes lies and sometimes tells the truth. Now the stranger is moseying along and hears three people talking. Of these three, one is a Knight, one is a Knave, and one is a Jester but naturally the stranger doesn’t know which one is which. Each makes one statement: A says, “I am a Jester.” B agrees, and says, “That is true.” C adds to the conversation by saing, “I am not a Jester.”
What are A, B, and C?
H. The stranger came upon three men sitting under a tree on a bench. One is a Knight, one is a Knave, and one is a Jester. The stranger asks the man on the far north end of the bench, whom we’ll call A, “What kind of man sits next to you?” A relplies, “He always tells lies.” Then the stranger asks the man in the middle, whom we’ll call B, “What kind of man are you?” and B replies, “I sometimes tell a lie and I sometimes tell the truth.” Then the stranger asked the man on the far south end of the bench, whom we’ll call C, “What kind of man is the one sitting next to you?” and C replies, “He always tells the truth.”
What are A, B, and C?
Note: The answers to these are given in full in the solution section instead of just the summary solution, as I normally do. For those lovers of the EK and/or Stefano Logic Problems, one or the other or both will appear again next month. What with my chemo and radiation, the truth is that I just seemed to have gotten behind and time got away from me - so I needed some 'ready-to-go' material to fill in. :-)