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Post by Kimmy on Dec 6, 2009 13:13:33 GMT
The train takes 18 minutes. The front of the train has to initially travel 10k to leave the tunnel, and then a further 0.5k until the rear of the train has left the tunnel - a total of 10.5k. Which takes 60 * (10.5 / 35) = 18 minutes.
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Post by Kimmy on Dec 6, 2009 13:16:48 GMT
I am away until Thursday.
Puzzle 4
What does this equation simplify to?
(x - a) * (x - b) * (x - c) * ... * (x - z) = ?
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Puzzle 5
We have been quite lucky with the weather recently, it has got steadily warmer each day, over the last five days. By this, I mean that the temperature rose by the same amount each day. The average temperature was 2 degrees C and I know it froze on two occasions. I also know the product of the temperatures was over 500 degrees but below 2,000 degrees and each temperature was an integer. What were the last 5 temperatures?
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Puzzle 6
Within the BrainBashers school, the science department has three disciplines. In total, 280 students study chemistry, 254 students study physics and 280 students study biology. 97 students study both chemistry and physics, 138 students study both physics and biology, 152 students study both chemistry and biology. 73 students study all three disciplines. Can you determine how many students there are in the science department? The answer is well below 814.
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Post by BC on Dec 6, 2009 13:31:46 GMT
I got one right, I got one right!! whooo hooooo!!  |
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Post by BC on Dec 8, 2009 0:44:34 GMT
Puzzle 6
573 ?
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Post by Kimmy on Dec 9, 2009 19:46:39 GMT
A lot of catching up to do so I shall just post the given answers.
4. 0: since one of the terms is (x - x).
5. The temperatures were -6, -2, 2, 6, 10 degrees C. Each day increased by a steady 4 degrees.
6. 500 students. The answer is most easily seen if three intersecting circles are drawn, and the numbers inside each section worked out.
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Post by Kimmy on Dec 9, 2009 19:47:13 GMT
Puzzle 7
My brother, Julian, is a little simple. I recently asked him to buy me some ribbon for my daughter's pretty pink bonnet. He went to the haberdashery shop for the required length but accidentally interchanged the feet and inches. When I measured the resulting ribbon I only had 5/8 of the length I required. How much ribbon did I originally ask for?
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Post by BC on Dec 10, 2009 11:12:29 GMT
Puzzle 7 7 feet 4 inches  |
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Post by Kimmy on Dec 11, 2009 9:30:21 GMT
I asked for 7 feet, 4 inches and my brother brought me 4 feet, 7 inches. If we label what I asked for as A feet and B inches, which is (12 x A + B) inches, then I actually received B feet and A inches, which is (12 x B + A) inches. Which means that:
(5 / 8) x (12 x A + B) = (12 x B + A)
Simplifying gives:
A = (91 / 52) x B
As B is the number of inches, it can only be between 1 and 12 and must give A as a whole number of feet. B = 4 is the only possible value, which means that A = 7. So I originally asked for 7 feet, 4 inches.
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Post by Kimmy on Dec 11, 2009 9:31:00 GMT
Puzzle 8
Many years ago, a cruise liner sank in the middle of the Pacific Ocean. The survivors luckily landed on a remote desert island. There was enough food for the 220 people to last three weeks. Six days later a rescue ship appeared, unluckily this ship also sank, leaving an additional 55 people stranded on the island to now share the original rationed food. The food obviously had to be re-rationed, but everyone was now on one-half of the original ration, so how many days in total would the food last for, from the day of the original sinking?
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Post by BC on Dec 11, 2009 11:06:53 GMT
Puzzle 8 Many years ago, a cruise liner sank in the middle of the Pacific Ocean. The survivors luckily landed on a remote desert island. There was enough food for the 220 people to last three weeks. Six days later a rescue ship appeared, unluckily this ship also sank, leaving an additional 55 people stranded on the island to now share the original rationed food. The food obviously had to be re-rationed, but everyone was now on one-half of the original ration, so how many days in total would the food last for, from the day of the original sinking? Here is my probably strange and erroneous thinking... Say the ration was 10 each a day. 10 x 220 people x 21 days = supply 46,200 6 days worth are consumed 46,200 / 21 days = 2,200 (amount eaten a day) 2,200 x 15 days = 33,000 supply remaining Now an additional 55 people = 275 33,000 / 275 = 120 per person Ration reduces to 5 120 / 5 = 24 daysBC ;D |
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Post by Kimmy on Dec 12, 2009 9:17:08 GMT
ANSWER 8.
30 days: originally there was enough food for 220 people for 21 days, which totals 4620 rations. After 6 days 1320 rations were eaten. Therefore there were now 3300 rations for 275 people, which would last for another 24 days at one-half ration per person. Which is 30 days in total from the original sinking.
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Post by Kimmy on Dec 12, 2009 9:17:34 GMT
Puzzle 10
A large fresh water reservoir has two types of drainage system. Small pipes and large pipes. 6 large pipes, on their own, can drain the reservoir in 12 hours. 3 large pipes and 9 small pipes, at the same time, can drain the reservoir in 8 hours. How long will 5 small pipes, on their own, take to drain the reservoir?
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Post by BC on Dec 13, 2009 18:46:53 GMT
Puzzle 10 A large fresh water reservoir has two types of drainage system. Small pipes and large pipes. 6 large pipes, on their own, can drain the reservoir in 12 hours. 3 large pipes and 9 small pipes, at the same time, can drain the reservoir in 8 hours. How long will 5 small pipes, on their own, take to drain the reservoir? 6 Big pipes takes 12 hours. Therefore each pipe would take 72 hours to drain the pool alone (i.e. 12 x 6). I think 9 big pipes are needed to drain in 8 hours. 3 big pipes and 9 small pipes drain the pool in 8 hours. Which means that 9 small pipes = 6 big pipes (ratio 1.5:1). So each small pipe will take 108 hours to drain the pool alone (72 x 1.5) So it will take small 5 pipes 21 hours and 36 minutes. I know its probably wrong. But at least I had a go!  |
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Post by Kimmy on Dec 14, 2009 9:55:39 GMT
Puzzle 10 A large fresh water reservoir has two types of drainage system. Small pipes and large pipes. 6 large pipes, on their own, can drain the reservoir in 12 hours. 3 large pipes and 9 small pipes, at the same time, can drain the reservoir in 8 hours. How long will 5 small pipes, on their own, take to drain the reservoir? 6 Big pipes takes 12 hours. Therefore each pipe would take 72 hours to drain the pool alone (i.e. 12 x 6). I think 9 big pipes are needed to drain in 8 hours. 3 big pipes and 9 small pipes drain the pool in 8 hours. Which means that 9 small pipes = 6 big pipes (ratio 1.5:1). So each small pipe will take 108 hours to drain the pool alone (72 x 1.5) So it will take small 5 pipes 21 hours and 36 minutes. I know its probably wrong. But at least I had a go! Thats whats its all about. Having a go. Its just a bit of fun AND IT PAID OFF. 21 hours and 36 minutes. The exact size of the pipes and reservoir does not matter. If we label the large pipes L, the small pipes S and if the reservior has a total of T litres, then: T / 6L = 12 which means L = T / 72 and T / (3L + 9S) = 8 which means that S = T / 108 we want T / 5S which gives 108 / 5 hours = 21.6 hours = 21 hours and 36 minutes.  |
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Post by Kimmy on Dec 14, 2009 9:56:23 GMT
Puzzle 11
A trout's tail weighs eight pounds. Its head weighs as much as the tail and one-half of the body combined, and the body weighs as much as the head and tail combined. What does the whole trout weigh?
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Post by BC on Dec 14, 2009 14:20:30 GMT
Puzzle 11 A trout's tail weighs eight pounds. Its head weighs as much as the tail and one-half of the body combined, and the body weighs as much as the head and tail combined. What does the whole trout weigh? On the ship-wreck-ration-days puzzle 8, I forgot to add the six days on that had already gone. Doh!  __________ More warped BC thinking no doubt... We know: T = 8 H = T + (1/2 B) B = H + T So, H = T + (1/2H + 1/2T) Double this a sec: 2H = 2T + (H + T) Now get rid of one H from each side: H = 2T + T (or H = 3T) As T = 8, we now know that H = 24 As B = H + T, B must be 32. 8 + 24 + 32 = 64 pounds. _____ Amended - got rid of a T too many first time 'round. |
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Post by Kimmy on Dec 15, 2009 7:48:15 GMT
ANSWER 11. 64 pounds: the head weighs 24 pounds, the body weighs 32 pounds and the tail weighs 8 pounds. |
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Post by Kimmy on Dec 15, 2009 7:48:43 GMT
Puzzle 12
My mother purchased 100 pounds of potatoes last week, which I knew to be exactly 99% water. After a week, drying in the sun, they had dried a little to become only 98% water. What was the total weight of the potatoes now?
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Post by BC on Dec 15, 2009 23:44:49 GMT
100 lbs = 1600 oz made up of P = 1% = 16 oz W = 99% = 1584 My simple brain is telling me to deduct 1% of W... i.e a further 16oz, therefore leaving 99lbs? I don't think that's right. P must remain at 16oz. It is only the W that reduces.  ----------- Try again. After the week drying in the sun, P now represents 2% of the total weight. We know that P = 2% = 16oz, then the remaining 98% = 784oz (i.e. 98 x 1/2P or 98 x 8) Add back P and you get 800oz or 50lbs. That sounds like too much of a reduction for just a 1% reduction in W doesn't it? However, 2% of 800 is 16. And 16 is what P must be. Aw gawd. -------------- OK, 50 lbs. Final answer.  |
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Post by Kimmy on Dec 16, 2009 12:07:33 GMT
50 pounds: in the original 100 pounds, 99% was water, therefore the potato element weighed 1% = 1 pound. After drying the potato element still weighed 1 pound, which was now 2% of the total (and 98% water). Therefore the total must be 50 pounds, 49 pounds of water and 1 pound of the potato element. |
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Post by Kimmy on Dec 16, 2009 12:08:10 GMT
Puzzle 13
Last week I spent half of my money on a new jacket and then I spent half of that amount on some new trousers. I was left with £32.94. How much did I spend?
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Post by BC on Dec 16, 2009 17:26:02 GMT
13. This one looks too easy. What am I missing?
£98.82
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Post by Kimmy on Dec 17, 2009 19:52:17 GMT
£98.82: I started with £131.76 and I spent £65.88 on a new jacket, and then £32.94 on the trousers, a total spend of £98.82. Not many having a go at these.  |
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Post by Kimmy on Dec 17, 2009 19:53:03 GMT
Puzzle 14
Once upon a time, and old lady went to sell her vast quantity of eggs at the local market.
When asked how many she had, she replied:
Son, I can't count past 100 but I know that.
If you divide the number of eggs by 2 there will be one egg left.
If you divide the number of eggs by 3 there will be one egg left.
If you divide the number of eggs by 4 there will be one egg left.
If you divide the number of eggs by 5 there will be one egg left.
If you divide the number of eggs by 6 there will be one egg left.
If you divide the number of eggs by 7 there will be one egg left.
If you divide the number of eggs by 8 there will be one egg left.
If you divide the number of eggs by 9 there will be one egg left.
If you divide the number of eggs by 10 there will be one egg left.
Finally. If you divide the Number of eggs by 11 there will be NO EGGS left!
How many eggs did the old lady have?
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Post by BC on Dec 17, 2009 22:09:09 GMT
Tough one. I shall ponder awhile. |
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Post by BC on Dec 18, 2009 3:38:27 GMT
Tough one. I shall ponder awhile. I have pondered awhile and must ponder no more. We know it's a multiple of 11, so I set up an excel spreadsheet and ran through the combinations, but after checking down to line 130ish - (i.e. 11x130), I gave up. All I can say is the old lady must have turned up with a lorry! ( unless I missed it, which is possible). BC |
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Post by Kimmy on Dec 18, 2009 10:29:38 GMT
25,201 eggs. This puzzle has a few different methods for finding the solution, one of which is:
Find a number X into which all of the numbers from 2 to 10 divide evenly. You can do this by simply using 2*3*4*5*6*7*8*9*10, but you can find a smaller number by finding the prime factors, a subset of which can be used to form any number from 2 to 10. 2*2*2*3*3*5*7 will do. This comes out to be 2520, and is the lowest number into which all the numbers 2-10 divide evenly.
We can add 1 to this number to satisfy the first 9 constraints of the puzzle (the remainder of 2521/2, 2521/3 ... 2521/10 is one), but this does not satisfy the last constraint, divisibility by 11.
Fortunately, we can multiply X (=2520) by any integer and add 1 and we will still satisfy constraints 1-9. So what Y do we multiply X by so that (X*Y) + 1 is divisible by 11. 2520/11 has a remainder of 1. Thus two 2520s divided by eleven would have a remainder of 1+1 = 2, and so forth...so ten 2520s divided by 11 would have a remainder of 10. This number plus one would divide eleven evenly, as well as also satisfy the first 9 constraints - thus 25201 is the answer.
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Post by Kimmy on Dec 18, 2009 10:30:22 GMT
Puzzle 15
I want to travel 1,000 miles on an adult tricycle and I have two spare tyres. However, I want to use all five tyres equally and have an equal mileage on each of the five tyres by the end of the trip. Of course I can only use three tyres at a time, so I will have to change tyres during the trip. At the end of the trip how many miles will each tyre have been used?
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Post by BC on Dec 18, 2009 14:18:32 GMT
Here's my stab at it:
If there were no spares, then the three tyres do 3000 miles (3x1000) collectively. So that is the total that the tyres have to do.
Two spares means the 3000 mile load is shared by 5 tyres.
3000 / 5 = 600 miles each
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Post by Kimmy on Dec 19, 2009 10:46:45 GMT
600 miles: a total of 1,000 miles have been travelled and at any one time, three tyres are travelling. Therefore 3,000 tyre miles have been travelled, which is shared equally by the 5 tyres. |
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