The idea for this logic problem is based on one sent to me by a visitor named Tatjana. I have no idea where she got the problem that she sent me to work, so I have made changes to all the conditions and most of the events, but used the same format. This way I don't infringe on any copywrited material. Thanks Tatjana! A bit of something different from the regular "run of the mill" logic problem I usually post. :-)
The first weekend in October is always set aside for the town’s Fall Festival, and Mr. Green is on the committee which schedules the events for each year. Lasting three days - Friday through Sunday - the committee scheduled eight events: a craft show, a fireworks display, an ice cream social, a parade, a picnic, a relay race, a talent contest, and a volleyball game. Each event was held during a different single time period - morning, afternoon, and evening, and no two events were held during the same time period. Later, Mr. Green sent a few facts about the festival to his friend, Dr. Gray, who enjoys working logic problems.
Mr. Green explained to Dr. Gray that even though one cannot exactly determine in which order each event was held from the ‘clues’ he was sending, he noted that one can determine the answer to a few conditions he set forth in his correspondence. Dr. Gray was able to determine each of the following eight conditions. Can you do the same?
Note: there are eight events scheduled, and nine time periods, so during one time period no event was scheduled at all. Unless specifically specified in one of the conditions, the period where no event is scheduled is not considered an event.
THE CLUES
a. The relay race was held in the morning.
b. The volleyball game was held after the parade.
c The craft show was the first event held.
d The talent contest was not held on Friday.
e. The fireworks display was held on Saturday evening.
f. The ice cream social took place took place in the evening, before the parade.
| FRIDAY | SATURDAY | *****SUNDAY***** | |
| MORNING | |||
| AFTERNOON | |||
| EVENING | ICE CREAM SOCIAL | FIREWORKS |
In the intro it says we cannot completely solve all the events which took place, but we can determine a couple of them. In the table directly above we’ll enter the info we know for sure. We see from the last clue that the fireworks is held on Sat. eve, so we enter that into the proper place. From Clue f, the ice cream social took place in the evening before the parade, and from Clue b, the volleyball game was held after the parade. Since it was in the evening, before the volleyball game, it couldn’t be on Sun. eve as no events occur on Mon. (intro), so the ice cream social is on Fri. eve. With these known facts, see if you can solve the following conditions. Note: It is important to read EXACTLY what the condition calls for. For example, in #4, some say "well, there might be a couple that could be true," but the conditions says that only ONE must be true; thus, there is only one answer.
THE CONDITIONS:
1. If the talent show is held the day before and at the same time of day, as the volleyball game, then which of the following must be true?
A The volleyball game is held Saturday afternoon.
B The relay race is held before the picnic.
C The talent show is held the same day as the picnic.
D The picnic is held Friday morning.
E The parade is held in the afternoon.
| FRIDAY | SATURDAY | *****SUNDAY***** | |
| MORNING | |||
| AFTERNOON | |||
| EVENING | ICE CREAM SOCIAL | FIREWORKS |
2. If the volleyball game is held on Sunday morning, then which one of the following is held on Saturday morning?
A. The picnic.
B. The parade.
C. The talent contest.
D. The relay race.
E. No event.
| FRIDAY | SATURDAY | *****SUNDAY***** | |
| MORNING | |||
| AFTERNOON | |||
| EVENING | ICE CREAM SOCIAL | FIREWORKS |
3. If exactly one event is held between the craft show and the parade, then the scheduling of how many events can be precisely determined.
A. 3
B. 4
C. 5
D. 6
E. 7
| FRIDAY | SATURDAY | *****SUNDAY***** | |
| MORNING | |||
| AFTERNOON | |||
| EVENING | ICE CREAM SOCIAL | FIREWORKS |
4. If the relay race is held on the same day as the volleyball game, then which one of the following must be true?
A. The picnic is held between the fireworks display and the relay race.
B. The picnic is held on Saturday afternoon.
C. Exactly two events are held between the volleyball game and the parade.
D. The talent contest is held the same day as the ice cream social.
E. The parade is held on Saturday afternoon.
| FRIDAY | SATURDAY | *****SUNDAY***** | |
| MORNING | |||
| AFTERNOON | |||
| EVENING | ICE CREAM SOCIAL | FIREWORKS |
5. If the volleyball game is held a day before and at the same time of day as the picnic, then which of the following must be true?
A. The ice cream social is held before the talent contest.
B. There is no event scheduled for Sunday evening.
C. The talent contest is held before the relay race.
D. The picnic is held on Saturday.
E. The parade is held on Sunday.
| FRIDAY | SATURDAY | *****SUNDAY***** | |
| MORNING | |||
| AFTERNOON | |||
| EVENING | ICE CREAM SOCIAL | FIREWORKS |
6. Each of the following is an acceptable schedule of events held on Sunday - Morning, Afternoon, Evening - EXCEPT:
A. Volleyball game, talent contest, picnic.
B. Relay race, talent contest, no event.
C. No event, volleyball game, talent contest.
D. Relay race, no event, talent contest.
E. No event, volleyball game, picnic.
| FRIDAY | SATURDAY | *****SUNDAY***** | |
| MORNING | |||
| AFTERNOON | |||
| EVENING | ICE CREAM SOCIAL | FIREWORKS |
7. If the parade is held on Sunday and before the picnic, which of the following is true?
A. No event is scheduled for Saturday afternoon.
B. The talent contest in held on Friday morning.
C. The volleyball game is held on Saturday.
D. The picnic is held the same day as the ice cream social.
E. The talent contest is held after the relay race.
| FRIDAY | SATURDAY | *****SUNDAY***** | |
| MORNING | |||
| AFTERNOON | |||
| EVENING | ICE CREAM SOCIAL | FIREWORKS |
8. If the talent contest, the picnic, and the relay race are all held on different day and at different times of the day, then the scheduling of how many events can be precisely determined.
A. 3
B. 4
C. 5
D. 6
E. 7
| FRIDAY | SATURDAY | *****SUNDAY***** | |
| MORNING | |||
| AFTERNOON | |||
| EVENING | ICE CREAM SOCIAL | FIREWORKS |
Back to Year to Year Logic Problem Page
For Everett Kaser lovers, this month Everett is taking a break, so to speak. He is hard at work (in real life!) on finishing up converting Descartes Enigma to his new program format and getting ready to start on Descartes Rainbow, a logic game which has been, up to now, only available to members of Kasergames. Soon it will be available to the general public. You can download his games (both registered and shareware versions) at www.kaser.com. Don't dispair, though, as he'll be back next month in a new logic problem! :-)
This puzzle is based on a three part logic problem submitted by a friend of mine from England - Mark Eustace - called the "Grecian Mystery." This is Part III of the logic problem. I hope you have enjoyed working it and I want to say "thanks tons, Mark!" for allowing me to use it on my site. I'm sure you'll see more of Mark's submissions here in the future.
In the previous two parts of this puzzle, Professor Silus Malvern and his nephew, Stefano, worked out how to open the ancient Greek relic called The Cube, recovered the golden key to the Tomb of Galista, and then worked their way through the complex and treacherous catacombs to reach the entrance to the Tomb. With heart pounding and hands shaking, Stefano’s Uncle Silus inserted the key in the door. It turned effortlessly and with a deep rumble, the door swung slowly open. Cautious of more traps, Silus and Stefano shone their torches around the tomb expecting to see the room awash with gold and jewels. Alas, they were disappointed - the room was almost empty. Each sat down at the entrance and studied the room.
On the floor in front of him, Silus found a small box. He opened it carefully and looked inside. There were instructions inside that told him what he needed to do to access the treasure. He carefully worked through the instruction and was able to work out various facts. These are set out below.
THE FACTS: There are 5 levers hidden in each of the north, east and west walls. These levers must be pulled in the correct order to open a secret trap door below the north wall. If any are pulled out of sequence, the door will never open and Galista's treasures will remain forever lost. Each lever is numbered one through five from left to right. Stefano’s uncle analysed the instructions, and in the end all their hard work and patience had paid off! Can you work out how to access the treasure?
1. The sequence to open the door rotates so that a lever is pulled from the north wall, then the east wall, and finally the west wall, before starting the next sequence again, beginning with another lever on the north wall.
2. No lever should be pulled in its sequence number; thus, a lever numbered 1 is not pulled first nor a lever numbered three, third.
3. No two levers of the same number should be pulled in any one north-east-west sequence, so if lever 1 is pulled for sequence 2 on the north wall, neither levers 2 on the east wall or west wall will be used in that sequence.
4. The numbers of levers used in the 2nd sequence add up to 12 and the numbers of the levers used in the 5th sequence add up to 7.
5. In the first sequence, the number of the lever used on the east wall is one lower than the number of the lever used on the west wall, but one greater than the number used on the north wall.
6. The three levers used in the third sequence are 1, 2, 5, but not in that order. In this sequence, the third lever pulled on the west wall was not 5.
7. One sequence starts with the lever numbered 1 on the north wall and is followed by the lever numbered 5 on the east wall.
8. In none of the five sequences needed to open the secret trap door are the same three numbered levers used, in any order.
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| SEQUENCE | NORTH WALL | EAST WALL | WEST WALL |