The 125 Best Brain Teasers of All Time Read online

  23.Call the trains A and B, and draw a sketch of where they are with respect to New York when the two meet. Look closely at your sketch.

  24.Say the words out loud as you see them laid out, starting with duck.

  25.Think of the phases of the day—dawn, noon, and twilight—as phases of human life.

  LEVEL 2: PRODIGY

  26.What state is a dormitory usually in? Neat, messy … ? What two-word phrase describes a typical dormitory at college?

  27.Traditionally, geometrical figures are classified as two-dimensional or three-dimensional. Does this help?

  28.The box must be one from which, after you have taken out one tie, you can easily determine the color of the other.

  29.Try a simpler version, with four balls. Then try it with five. Do you see any pattern?

  30.Always count the number of butts and remember that three of them equal a new cigarette.

  31.There are six steps between iron and lead.

  32.Figure out where Claudio might stand in relation to the others.

  33.Consider the opposite: How many sisters does the brother have? Does this help?

  34.Keep in mind that each successive number increases “exponentially.”

  35.Look at the letters that are the same, and start with those, trying out logical number substitutions.

  36.Again, examine the letters that are the same, and start with those.

  37.Consider the meaning of one of the two verbs in the statement.

  38.When you have been waiting a while, you might end up saying “It has been a long …”

  39.Start by unscrambling the easy ones—WOT and OD.

  40.Again, start with the easy ones.

  41.Take a sampling and count the 1s in each sample: the numbers from 1 to 9, from 10 to 19, and so on.

  42.Start by pouring water from the 5-gallon container.

  43.Simplify by turning “father’s father’s son” into a clearer expression.

  44.The two are four-letter words.

  45.Try out a few alternatives first.

  46.Take out some coins and see how they can be combined into different values.

  47.The book is a well-known one by Dr. Seuss.

  48.Consider the statements that say, more or less, the same thing, in figuring out if they are likely to be true or false.

  49.Translate “Duma” into English, focusing on what it could mean under the circumstances.

  50.Like other doublets, make your first change to reflect what’s to come.

  LEVEL 3: BRAINIAC

  51.Don’t forget that shoes have an orientation, so a match will involve a right-foot and a left-foot, not just the same color.

  52.Where is the snail in relation to the bottom of the well on the 26th day? Take it from there.

  53.Recall that Princess Diana died in an automobile accident.

  54.Always start the sequencing with the person who comes in right after someone else; then add the rest later.

  55.The word bee should give it away.

  56.Historically, one part of the newly formed word means “outer space.”

  57.Think of what part of a truck can be altered easily and temporarily.

  58.An alternate meaning of the desired word is “just.”

  59.If you divide something by 3, then you are dividing it into groups. So, for example, 6 socks divided by 3 makes 2 groups of 3 socks each.

  60.If any villager is asked, “Are you a truth-teller?” what answer would a truth-teller give? What answer would a liar provide?

  61.Each letter is the first in a series of words logically connected to each other.

  62.Again, each letter is the first in a series of words that are logically connected.

  63.These letters stand for words in a saying.

  64.Replace event with date.

  65.Let the brick’s weight be x, and take it from there.

  66.An opposite for the word meaning “perspicuity” is obscurity.

  67.As in all sequences, figure out the value by which each successive number increases.

  68.Start by eliminating couples with the same color clothing.

  69.Carefully inspect the letters in each word.

  70.Figure out who lied first.

  71.You may have to try out a few possibilities. Just use your basic math sense.

  72.Again, you may just have to try out a few possible combinations of signs.

  73.The word meaning “paramour” can also mean “darling.”

  74.The word meaning “caring” can also mean “sensitive.”

  75.Figure out who the violinist is first, as this is the easiest to determine.

  LEVEL 4: MASTERMIND

  76.If you are having difficulty envisioning a solution, take two coins (such as two quarters) and revolve one around the other, tracing the movement with a pencil on a sheet of paper below the coins. Then take a look at the tracing.

  77.Draw a vertical number line, placing the firefighter at 0 as the mid-point. Then count from there, going up and down the line.

  78.As in the other racing puzzles, start by placing someone who comes right after someone else and work from there.

  79.With all puzzles of this type, try a few calculations to narrow down the candidate numbers. After some trial and error, a pattern may emerge that will allow you to envision the answer.

  80.Again, try a few calculations with prime numbers to narrow down the ones that are potential candidates. Trial and error may help.

  81.As before, remember to apply worst-case scenario reasoning.

  82.Again, apply worst-case scenario logic.

  83.As with other puzzles in this genre, try a few calculations to narrow down the candidate numbers.

  84.Here we go again: Try a few calculations to narrow the field of candidate numbers.

  85.Yet another example: Try a few calculations to narrow down the candidates.

  86.Rephrase “sister’s nephew” and “man’s son” in different ways. This might help you untangle the connection of these relations.

  87.Rephrase “[Mary’s] mother’s grandson” in your own words. Again, this might help you unravel the relationships.

  88.Again, rephrase the confusing statements into your own words. This allows you to envision the relations more concretely.

  89.There are six steps between the two words.

  90.Set up a chart with all possibilities, and take it from there.

  91.There are six steps.

  92.The best way to decode a cryptogram is to figure out what word or words are the most likely to occur first in an English sentence, such as articles and demonstratives.

  93.First figure out the uphill and downhill rates as two separate speeds.

  94.A synonym for the word meaning “shred” is grind.

  95.A synonym for the word meaning “inventive” is imaginative.

  96.A synonym for the word meaning “fatherly” is protective.

  97.Remember that a pair of socks must match not only in color but also in orientation (right-foot and left-foot).

  98.Figure out what the two probabilities are together.

  99.Rephrase “this man’s son” and “my father’s son” in your own words. As always, this might help you unravel the relation involved.

  100.Set up a timeline or chart for the required weeks, and indicate the days when Jason works and the days when Alicia works. It will then be easy to see when these two line up with each other.

  LEVEL 5: GENIUS

  101.Think of the various possibilities for placing the 0, since it is a unique number with unique properties.

  102.The letter A has been replaced here with the number 26.

  103.Set up a diagram showing different positions for the trains.

  104.For each option, calculate your salary at the end of each year.

  105.As in the case of puzzle 49, translate “Ruma” logically into English.

  106.Start with the contradictory statements—one of which will be true and the other false.

  107.
Set up a sequence, moving from left to right, in which the numbers are placed according to the given statements. You may have to try out a few possibilities.

  108.Set up a table showing the possible outcomes of the two dice for throwing a 6 or a 7.

  109.Make the following substitution: Who am I = What day (today, yesterday, tomorrow, and so on) am I?

  110.There are several ways to solve this, but as in puzzle 20, the first trip over is the crucial one. How does the traveler start his journey: with the wolf, the Wolf-Eater, the goat, or the cabbage?

  111.There are five steps.

  112.There are six steps.

  113.There are 10 steps.

  114.One of the letters in the word is I, which is the roman numeral for 1.

  115.Set up the numbering of the houses in categories: houses 1 through 9, houses 10 through 19, and so on.

  116.Notice that there is something specific about the shape of the letters.

  117.There are 13 steps.

  118.Who is the daughter’s mother in this case? Rephrase it in your own words.

  119.Consider the position of 0, since it has special properties.

  120.A synonym for the word meaning “opposition to” is struggle.

  121.A synonym for the word meaning “inferences” is conclusions.

  122.The 1s can be digits in a number.

  123.As in all these sequences, figure out how the value of each successive number is determined. In this case, look at the actual digits of each number.

  124.Determine who the liars are by comparing statements that say the same thing.

  125.Enter the mind of the woman who solved it, and reason as she did.

  ANSWERS

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  LEVEL 1: SMARTYPANTS

  1.Spot—Spit. By changing the o in spot (stain) to i, you will get spit (saliva).

  2.The rearranged word is married. Successfully married people are also admirers of each other, aren’t they?

  3.A quarter (25 cents) and two dimes (20 cents). No further explanation is needed, correct?

  4.The man is the girl’s father. Her father’s mother-in-law is his wife’s mother, and his wife is the girl’s mom.

  5.Bob = engineer, Janet = accountant, Shirley = director. We know that Bob has a brother, so he is not the accountant, who is an only child. And Shirley earns more than someone else (the engineer, to be exact), so she is also not the accountant, who earns the least. Who does this leave for the accountant position? The only possibility is Janet. We are told that Shirley earns more than the engineer, so she cannot be the engineer. What’s left for Shirley then? She isn’t the accountant or the engineer, so she must be the director. The final position of engineer is therefore held by Bob based on the process of elimination.

  6.(1) friendship (friend = companion, ship = sailing vessel), (2) bookstore (book = volume, store = retail establishment), (3) greenhouse (green = leaf color, house = abode), (4) lookout (look = gaze, out = away)

  7.Gina. Let’s represent the outcome as follows: Gina—Frieda—Hannah. This shows that Frieda beat Hannah but not Gina, which means that Gina came in ahead of Frieda.

  8.Gasoline is the odd one out because it is a liquid; the others are solids.

  9.The letters represent the first letters in the days of the week: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday.

  10.Lisa drank ¾ pint. If Lucy drank 6 pints, then Bill drank half of this, which is 3 pints; Arnie drank half of this amount, or 1½ pints; and Lisa drank half of this, or ¾ pint.

  11.Three draws. Suppose the first ball you draw out is a white one. If you’re lucky the next ball you draw out will also be white, and it’s game over! But you cannot assume this luck-based scenario. You must, on the contrary, assume the worst-case scenario; this means that the next ball you draw out is black. Thus, after two draws, you will have taken out of the box one white ball and one black ball, under the worst-case scenario. Obviously, you could have drawn out a black ball first and a white one second. The end result would have been the same: one white and one black ball after two draws irrespective of order. Now, the next draw—the third one—will be either a white or black ball (that’s what is in the box). Either way, that third ball will match one of the other two already outside. If it is white, it matches the white ball outside; if it is black, it matches the black ball outside.

  12.Four draws. The reasoning for the 30-ball, three-color version is the same. You start by assuming the worst-case scenario. What is that? It consists of drawing out three balls of three different colors—white, black, and red, in any order. Now, keep in mind that these three balls of different colors are now outside the box. The fourth ball you draw out—no matter what color—will match one of the three colors outside the box, since it can only be white, black, or red.

  13.Bird: jailbird, birdcage, birdbrain, birdcall, birdsong.

  14.89. Each number, starting with the third one, is the sum of the previous two.

  15.39. Each successive number increases by one more than the last. So, 3 increases by one to produce 4; 4 increases by two (one more) to produce 6; 6 increases by three (one more from the last) to produce 9; and so on.

  16.Kayak.

  17.Rotator.

  18.40 feet. The trout is 20 feet plus half its length. Let’s say its length is x, so, its full length is: x = ½ x + 20. This says that the total length (x) equals 20 feet plus half the overall length (½ x). Solving for x we get 40.

  19.The steps are as follows: COLD—(1) cord—(2) word—(3) ward—WARM.

  20.Three back-and-forth trips and one final one-way trip over at the end. The traveler cannot start with the wolf, since that would leave the goat alone with the cabbage, and the goat would eat it. Also, the traveler cannot start with the cabbage, since that would leave the wolf and goat alone, and the wolf would eat the goat. So, practically speaking, the traveler can only start by taking the goat with him on the boat to the other side, leaving the wolf safely with the cabbage on the original side. After dropping off the goat on the other bank, he then rows back alone. This constitutes his first round trip. Back on the original side, he picks up the wolf and rows with it to the other side, leaving the cabbage behind. Upon reaching the other bank he drops off the wolf, but rows back with the goat, so that the wolf cannot eat the goat for lunch. Again, this decision is just common sense, and constitutes the traveler’s second round trip. Back on the original side, he leaves the goat there, and this time, takes the cabbage with him on the boat. When he reaches the other bank, he drops off the cabbage, leaving the wolf and cabbage safely together, as he rows back alone. This is his third round trip. He then picks up the goat on the original side and rows across with it. When he reaches the other bank he will have his wolf, goat, and cabbage intact and can finally continue on with his journey.

  21.Life. The two words created are wildlife and lifestyle.

  22.The eraser costs 2½ cents. This means that the pencil costs 52½ cents, which is 50 cents more than the eraser. When you add the two together, the total is 55 cents.

  23.Neither train will be nearer to New York. They will be the same distance from the city. The trick in this puzzle is the word meet. Everything else in the puzzle is useless information. Obviously, when the two trains meet, neither train will be nearer to New York, even though they are going in different directions.

  24.Duck under the bridge, with duck referring to the verb meaning “lower the head or the body to avoid a blow.”

  25.The fearless Oedipus answered: “Humans, who crawl on all fours as babies (the dawn of life), then walk on two legs as grown-ups (the noontime of life), and finally need a cane in old age (the twilight of life) to get around.” Upon hearing the answer, the astonished Sphinx killed itself, and Oedipus entered Thebes as a hero. Ironically, by solving the riddle, the devastating prophecy Oedipus had tried to elude came true—a divination that he would kill his father (a crime he had unwittingly committed on the way to Thebes) and marry his mother, the widowed queen of Thebes.
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br />   LEVEL 2: PRODIGY

  26.Dirty room. It’s fascinating how words are connected to each other, isn’t it? Maybe the ancients were right after all, believing that anagrams reveal unexpected truths about the world. Bizarre!

  27.Cube is the odd one out because it is a three-dimensional figure; the others are all two-dimensional.

  28.The actual contents of each box can be determined in just one drawing if that drawing is made from the box labeled BW. All three labels are incorrect. So, the contents of the one labeled BW should actually be either BB or WW. If you draw out a black tie, then its contents are, of course, BB; alternatively, if you draw out a white tie, then its contents are WW. Either way, you will have identified its contents. The contents of the other two boxes can now be easily determined. It all depends on which color you draw from the box labeled BW. Here are the two possibilities:

  Scenario 1: The BW box is mislabeled. It really contains two black (BB) or two white (WW) ties. Assume that from the BW box you draw out a black tie (B). This means that its contents are BB (the two black ties). Now consider the WW box, which is also mislabeled. It will contain either BW or BB (not WW, of course, as its wrong label claims). It cannot contain BB, since the first one does, as just deduced. So, it must contain BW. By elimination, the third box, mislabeled BB, contains WW.

  Scenario 2: Again, the BW box is mislabeled. It really contains two black (BB) or two white (WW) ties. Assume this time that you draw out a white tie (W). This means that its contents are WW (the two white ties). Now consider the BB box, which is also mislabeled. It will contain either BW or WW (not BB of course). It cannot contain WW, since the first one does, as just deduced. So, it must contain BW. By elimination, the third box, mislabeled WW, contains BB.

  29.Take three balls and place them on the left pan. Take three others and place them on the right pan. Put the remaining seventh ball on the table. Now, consider the scale. If the pans balance, then the six balls are all the same weight, meaning that the ball on the table is the culprit ball. However, we can’t assume this very fortunate outcome. As in most puzzles of this kind, we must assume a worst-case scenario, since we are asked to weigh the balls no more than twice. So, let’s assume that one of the pans goes up, indicating that it contains the culprit ball. Let’s eliminate the other three balls. Now, for our second time on the scale, we take the three balls on the pan that went up, put one on the table, and each of the other two on separate pans. There is only one possible outcome left. If the pans balance, then the ball on the table is the culprit ball. If one of the pans goes up, then it contains the culprit ball. Either way, in weighing the balls two times, we are now sure we have identified the ball that weighs less.