Home » General Chat » Circular File » Puzzle thread Dec. 29
 Puzzle thread Dec. 29 |
Mon, 29 December 2003 21:24  |
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 Ron |
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Here are this week's puzzles. 24 hour deadline, PM me your answers. Get 5 puzzles correct to get one chance to win the title Weekly Puzzle Master, get all 6 correct to get two chances.
1. Can you replace the missing digits in the number 789XYZ so that the resulting number is divisible by 7, 8, and 9? The only restriction is that you cannot use a 7, 8, or 9.
2. A hiker went on a hike. The first part of the trip was on level ground, and he walked at 4 miles per hour. The second part was uphill, and his speed slowed to 3 mph. He then retraced his steps going 6 mph downhill and then the same 4 mph back to his starting point. Given that the total trip took 5 hours, how far did the hiker walk?
3. The cost of hiring a private rail carriage is shared equally by all the passengers. The carriage has seats for 40 passengers and the total bill amounts to $70.37. How many passenger seats are not occupied?
4. What number should replace the question mark?
|---------------|
| 9 | 4 | 6 |11 |
|---------------|
| 3 | 6 | 7 | 4 |
|---------------|
| 5 | ? | 4 | 1 |
|---------------|
|11 | 6 | 3 | 8 |
|---------------|
5. Following the rule of the sequence of numbers, what number should come next?
1, 4, 7, 11, 15, 13, 17, ?
6. Although it doesn't have the cachet of some of the other competitions at the State Fair, the battle for the title of Handsomest Animal is always fierce. This year, each of the top five finishers was a different type of animal, and each animal's ower (three of whom - Alma, Carolyn, and Dawn - are women, and two of whom - Bob and Ed - are men) hailed from a different town. From the information provided, determine the animal (one is a pig) that placed in each position, the first and last names of its owner, and the town (one is Gravel Run) from which its owner hails.
1. The lamb, which didn't win 5th prize, placed behind the animal owned by one surnamed Gates.
2. The animal whose owner lives in Rocky Rill did not win 1st prize.
3. The animal owned by the one s
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Ron Miller
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| Re: Puzzle thread Dec. 29 |
Tue, 30 December 2003 21:43  |
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| Ron |
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Four people got at least 5 puzzles answers correct: Ashlyn, mazda, overworked, and Sinla
One of the above got all 6 puzzles correct.
And the RNG picks overworked as this weeks Puzzle Master.
Here are the answers.
1. 789264
Note that 7x8x9=504. Upon dividing 789000 by 504, you get a remainder of 240. Therefore, if you add 504-240=264 to 789000, you get the desired number: 789264. This answer is unique because the only other member of the form 789.XYZ to be divisible by 504 is 789264+504=789768, which repeats both the 7 and the 8.
2. Let x = the total distance traveled, and y = the uphill (or downhill) distance. Because time = distance/speed, the total time traveled is given by 2(((x/2)-y)/4)+(y/3)+(y/6), the factor of 2 reflecting the fact that the level portion of the trip was hiked twice.
Therefore 2(((x/2)-y)/4) + (y/3)+(y/6) = 5, which looks like one equation with two unknowns, but in fact the y terms all cancel out, leaving (x/4) = 5, or x=20. The length of the trip was thus 20 miles. (for those who used a computer program to solve for you, the above shows one way how to solve it)
3. 9 seats were empty. 31 people pay $2.27 each. Alternate answer: 39 seats empty, 1 person paying $70.37.
4. 8. Looking along each row AND down each column the sums of alternate numbers are the same.
5. 24. The numbers, spelled out, follow the numerical sequence: 3-4-5-6-7-8-9-10. 24 spelled out has 10 letters.
6.
1st, rooster, Alma Gates, Gravel Run
2nd, lamb, Bob King, Pebble Pond
3rd, goat, Ed Johnson, Boulder
4th, calf, Carolyn Hill, Stonybrook
5th, pig, Dawn Farmer, Rocky Rill
Thread unlocked.
...
Ron Miller
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| Re: Puzzle thread Dec. 29 |
Wed, 31 December 2003 02:18 |
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| HiltonL |
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Messages: 67
Registered: December 2003
Location: South Africa | |
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Congrats overworked!
| Ron wrote on Tue, 30 December 2003 04:24 |
5. Following the rule of the sequence of numbers, what number should come next?
1, 4, 7, 11, 15, 13, 17, ?
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Ron, why doesn't the sequence go 1, 4, 3, 11, 15, 13, 17?
Just a thought, since "three" has 5 letters and comes before "seven" which has 5 letters.
Cheers
Hilton
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| Re: Puzzle thread Dec. 29 |
Wed, 31 December 2003 15:33 |
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| HiltonL wrote on Wed, 31 December 2003 02:18 |
Congrats overworked!
| Ron wrote on Tue, 30 December 2003 04:24 |
5. Following the rule of the sequence of numbers, what number should come next?
1, 4, 7, 11, 15, 13, 17, ?
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Ron, why doesn't the sequence go 1, 4, 3, 11, 15, 13, 17?
Just a thought, since "three" has 5 letters and comes before "seven" which has 5 letters.
Cheers
Hilton
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Thank you.
And congratulations to my peers who also got 5 or more of the answers right.
I also mentioned the sequence oddity to Ron.
- Kurt
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