Clever Puzzles

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A conference room contains three separate wallmounted spotlights – right, left and front of stage. Each is controlled by its own onoff switch. These three switches are numbered 1, 2 and 3, but they are in a backroom which has no sight of the the spotlights or the conference room (and there are no reflections or shadows or mirrors, and you are alone). How do you identify each switch correctly – right, left, front – if you can only enter the backroom once?
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An art gallery features a modern work of ‘moving art’. The artist stands by a stack of paintings, each featuring a different number. One of the paintings is displayed on the wall. At certain times the artist removes the painting from the wall and replaces it with a painting from the stack. At 11am, the artist hangs a painting of the number 30. At 4pm he hangs a painting of number 240. At 7.30pm he hangs a painting of number 315. What painting does the artist hang at 9.20pm?
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Here’s a new kind of coded puzzle for you to try – a cryptolist! The list of words below all relate to the topic of ‘what’s for supper’. The code used for each word is the same. For example, if you determine that the letter A is really the letter E in the first word, this is true for every word in the list.
Solving Tips
A cryptogram is a message written in a code where each letter has been substituted with a different one. For example, BCCX LCTAEAB can be decoded to read GOOD MORNING where the B stands for G, the C stands for O, the X stands for D, etc.. No letter can stand for itself and no letter can represent multiple letters.
Hint: Look for similarities in words, for example THE, THERE, THEIR, THEY, and THEN. Also, look for repetitions in single and double letters, for example E, R, S, T, and LL are all common letters.View SolutionSubmit Solution 1,523.5K views
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Also known as Hempel’s Paradox, for the German logician who proposed it in the mid1940s, the Raven Paradox begins with the apparently straightforward and entirely true statement that “all ravens are black.”
The paradox here is that Hempel has apparently proved that seeing an apple provides us with evidence, no matter how unrelated it may seem, that ravens are black. It’s the equivalent of saying that you live in New York is evidence that you don’t live in L.A., or that saying you are 30 years old is evidence that you are not 29. Just how much information can one statement actually imply anyway?
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Imagine that a farmer has a sack containing 100 lbs of potatoes. The potatoes, he discovers, are comprised of 99% water and 1% solids, so he leaves them in the heat of the sun for a day to let the amount of water in them reduce to 98%. But when he returns to them the day after, he finds his 100 lb sack now weighs just 50 lbs. How can this be true? Well, if 99% of 100 lbs of potatoes is water then the water must weigh 99 lbs. The 1% of solids must ultimately weigh just 1 lb, giving a ratio of solids to liquids of 1:99. But if the potatoes are allowed to dehydrate to 98% water, the solids must now account for 2% of the weight—a ratio of 2:98, or 1:49—even though the solids must still only weigh 1lb. The water, ultimately, must now weigh 49lb, giving a total weight of 50lbs despite just a 1% reduction in water content. Or must it?
Although not a true paradox in the strictest sense, the counterintuitive Potato Paradox is a famous example of what is known as a veridical paradox, in which a basic theory is taken to a logical but apparently absurd conclusion.
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In his final written work, Discourses and Mathematical Demonstrations Relating to Two New Sciences (1638), the legendary Italian polymath Galileo Galilei proposed a mathematical paradox based on the relationships between different sets of numbers. On the one hand, he proposed, there are square numbers—like 1, 4, 9, 16, 25, 36, and so on. On the other, there are those numbers that are not squares—like 2, 3, 5, 6, 7, 8, 10, and so on. Put these two groups together, and surely there have to be more numbers in general than there are justsquare numbers—or, to put it another way, the total number of square numbers must be less than the total number of square and nonsquare numbers together. However, because every positive number has to have a corresponding square and every square number has to have a positive number as its square root, there cannot possibly be more of one than the other.
Confused? You’re not the only one. In his discussion of his paradox, Galileo was left with no alternative than to conclude that numerical concepts like more, less, or fewer can only be applied to finite sets of numbers, and as there are an infinite number of square and nonsquare numbers, these concepts simply cannot be used in this context.
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