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"Light" Riddles - Final 6 of 196
Riddle:
Julie is going on an extended trip for three weeks. She lives in a remote area where there are frequent electrical power outages which can last up to three or four days. Julie has quite a bit of food in her freezer which would go bad if it thawed and then re-froze. She does have digital clock and a VCR which would flash 12:00 if the power went out. Unfortunately the clock and VCR flash even if the power only goes out for a few seconds. What can Julie do so that when she returns home she will be able to determine whether the power was out long enough to thaw her food? Asking a neighbor whether the power was out, isn't a reliable option because the nearest house is half a mile away, and one house may have power, while another house may have no power. She won?t be able to have a neighbor check on her house every day, and has no one to house sit.
Answer: One thing Julie could do is freeze a tray of ice-cubes, and turn the tray of ice upside down in her freezer. When she comes home, she should check the tray. If the ice cubes are still in the tray, the food is safe to eat. If the trays are empty, it's time to clean out the freezer. She will have to make a judgment call if the ice-cubes are only slightly thawed.
Riddle:
There are 100 light bulbs lined up in a row in a long room. Each bulb has its own switch and is currently switched off. The room has an entry door and an exit door. There are 100 people lined up outside the entry door. Each bulb is numbered consecutively from 1 to 100. So is each person. Person No. 1 enters the room, switches on every bulb, and exits. Person No. 2 enters and flips the switch on every second bulb (turning off bulbs 2, 4, 6, ...). Person No. 3 enters and flips the switch on every third bulb (changing the state on bulbs 3, 6, 9, ...). This continues until all 100 people have passed through the room. What is the final state of bulb No. 64? And how many of the light bulbs are illuminated after the 100th person has passed through the room?
Answer: First think who will operate each bulb, obviously person #2 will do all the even numbers, and say person #10 will operate all the bulbs that end in a zero. So who would operate for example bulb 48: Persons numbered: 1 & 48, 2 & 24, 3 & 16, 4 & 12, 6 & 8 ........ That is all the factors (numbers by which 48 is divisible) will be in pairs. This means that for every person who switches a bulb on there will be someone to switch it off. This willl result in the bulb being back at it's original state. So why aren't all the bulbs off? Think of bulb 36:- The factors are: 1 & 36, 2 & 13, 6 & 6 Well in this case whilst all the factors are in pairs the number 6 is paired with it's self. Clearly the sixth person will only flick the bulb once and so the pairs don't cancel. This is true of all the square numbers. There are 10 square numbers between 1 and 100 (1, 4, 9, 16, 25, 36, 49, 64, 81 & 100) hence 10 bulbs remain on.
Riddle:
You are given a set of scales and 12 marbles. The scales are of the old balance variety. That is, a small dish hangs from each end of a rod that is balanced in the middle. The device enables you to conclude either that the contents of the dishes weigh the same or that the dish that falls lower has heavier contents than the other. The 12 marbles appear to be identical. In fact, 11 of them are identical, and one is of different weight. Your task is to identify the unusual marble and discard it. You are allowed to use the scales three times if you wish, but no more. Note that the unusual marble may be heavier or lighter than the others. How can you identify it and determine whether it is heavy or light?
Answer: Number the marbles from 1 to 12. For the first weighing put marbles 1,2,3 and 4 on one side and marbles 5,6,7 and 8 on the other. The marbles will either they balance or not. If they balance, then the different marble is in group 9,10,11,12. Thus, we would put 1 and 2 on one side and 9 and 10 on the other. If these balance then the different marble is either 11 or 12. Weigh marble 1 against 11. If they balance, the different marble is number 12. If they do not balance, then 11 is the different marble. If 1 and 2 vs 9 and 10 do not balance, then the different marble is either 9 or 10. Again, weigh 1 against 9. If they balance, the different marble is number 10, otherwise, it is number 9. That was the easy part. What if the first weighing 1,2,3,4 vs 5,6,7,8 does not balance? Then any one of these marbles could be a different marble. Now, in order to proceed, keep track of which side is heavy for each of the following weighings. Suppose that 5,6,7 and 8 is the heavy side. We now weigh 1,5 and 6 against 2,7 and 8. If they balance, then the different marble is either 3 or 4. Weigh 4 against 9, a known good marble. If they balance then the different marble is 3 or 4. Then, if 1,5 and 6 vs 2,7 and 8 do not balance, and 2,7,8 is the heavy side, then either 7 or 8 is a different, heavy marble, or 1 is a different, light marble. For the third weighing, weigh 7 against 8. Whichever side is heavy is the different marble. If they balance, then 1 is the different marble. Should the weighing of 1,5 and 6 vs 2,7 and 8 show 1,5,6 to be the heavy side, then either 5 or 6 is a different heavy marble or 2 is a light different marble. Weigh 5 against 6. The heavier one is the different marble. If they balance, then 2 is a different light marble.
Riddle:
A woman is walking down a street night at a constant pace. As she passes the street light, she notices that her shadow becomes longer. Does the top of her shadow move faster, slower or the same when the shadow is longer as when it is shorter?
Answer: This point maintains a constant speed, independent of the lenght of the shadow.
Riddle:
Jack has 8 bricks, 7 of them weigh the same but one is slightly heavier. Using a balance scale, how can Jack find the heavier brick in two weighings?
Answer: First, he splits them into piles of 3, 3, and 2 bricks.
Then, he weighs both groups of 3 with each other. If they balance he knows the brick is one of the 2 unweighed bricks and he can weigh them to find the heavier one.
If the stacks of 3 bricks do not balance, he will weigh 2 of the 3 bricks.
If they balance he will know the brick left unweighed is heavier, or if they do not balance, he will find the heavier one.
Riddle:
There is a man stood on top of a mountain frozen holding a peice of straw. How did he get there?
Answer: He was with his friend in a hotair balloon when they were about to hit a mountin so they took of there clothes to make it lighter so they would go higher but it wasnt working so they drew straws and who ever had the shortest straw would have to jump out so he was the one who picked the shortest straw.
