The 125 Best Brain Teasers of All Time Read online

  30.40 cigarettes. Jack smoked the 27 cigarettes he took out from his pocket. Since he smoked only ⅔ of a cigarette, he therefore would leave a butt equal to ⅓ of a cigarette. So, for every 3 cigarettes he smoked, he was able to piece together a new cigarette ⅓ butt + ⅓ butt + ⅓ butt = 1 new cigarette). After smoking the original 27 cigarettes, he was thus able to make 9 new cigarettes. If you stopped here, simply adding 27 (number of cigarettes Jack smoked originally) + 9 (number of new cigarettes made and smoked by Jack) = 36 (total number of cigarettes), you forgot that smoking the 9 new cigarettes also produced butts. In fact, Jack’s 9 new pieced-together cigarettes produced 9 new butts of their own. From these 9 butts, Jack was able to make, of course, 3 more cigarettes (3 butts = 1 new cigarette). So, in addition to the 9 new cigarettes Jack made from the original 27, he was also able to make 3 more from those 9 pieced-together ones. But, then, those 3 extra cigarettes produced 3 butts of their own, from which Jack was able to make yet 1 more cigarette. Altogether, therefore, Jack smoked 27 + 9 + 3 + 1 = 40 cigarettes before giving up his bad habit.

  31.Iron—(1) icon (change the r in iron to c)—(2) coin (rearrange the letters in icon)—(3) corn (change the i in coin to r)—(4) cord (change the n in corn to d)—(5) lord (change the c in cord to l)—(6) load (change the r in lord to a)—Lead (change the o in load to e). In summary: IRON—icon—coin—corn—cord—lord—load—LEAD. Another possible solution is IRON-icon-coin-loin-loan-lean-LEAD.

  32.As for the other puzzles in this genre, the final order reflects all the statements. The only order that works (using the players’ initials: A = Armand, C = Claudio, S = Shirley, D = Dina, E = Elgin) is A—S—D—E—C. Translate this into the statements made and you will see that it holds.

  33.Frank has four children—three daughters and one son, who is, of course, a brother to the three sisters.

  34.729. The numbers increase as powers of 3: 31 (= 3), 32 (= 9), 33 (= 27), and so on.

  35.T = 3, I = 1, P = 2, A = 5. TIP + PIT = APA: 312 + 213 = 525. These numerical substitutions are the ones that work mathematically—the solver simply has to do the substitutions to see it.

  36.S = 4, L = 5, O = 0, B = 1, K = 6: SLOB + BLOL = KOOK: 4501 + 1505 = 6006. These substitutions are the ones that work mathematically, as in number 35. Another possible solution is 4503 + 3505 = 8008.

  37.Only one. Only one person was going to St. Ives—the narrator of the rhyme. If you read carefully, you’ll see it never says which direction the kits, cats, sacks, and wives were going. In fact, they were coming from St. Ives, moving in the opposite direction from the narrator!

  38.Time. Time is indeed both long and short, and so on, as Voltaire points out.

  39.Two wrongs do not make a right.

  40.To err is human; to forgive, divine.

  41.1. The digit occurs once in each of the numbers from 11 to 19, and also in every subsequent set—21, 22 … ; 31, 32 … . Logically, it appears more than any other number.

  42.First, Mark fills the 5-gallon container. He pours 3 gallons of it into the 3-gallon container, filling it up; the remaining 2 gallons he then pours into the 10-gallon container. He then fills up the 5-gallon container with water again and adds this to the 10-gallon container, thus producing the required 7 gallons in the 10-gallon container.

  43.Father. The father’s father is Beverley son’s grandfather. The son of the grandfather is, of course, the father himself.

  44.Lead–Deal: To lead is to guide someone (definition 1) and a deal is a bargain (definition 2).

  45.One of each. Mary has just three pets: She has one dog, one cat, and one rabbit. This works out perfectly, since all her pets except two (3 − 2; that is, 1) are supposed to be dogs. And, indeed, she has one dog. Similarly, she has 3 − 2 (that is, 1) cat, and 3 − 2 (that is, 1) rabbit.

  46.7 dimes and 13 nickels. First, assume that Alex has an equal number of dimes and nickels in his pocket—10 of each. How much money does that make? Well, 10 dimes add up to $1, and 10 nickels to 50 cents, for a total of $1.50. The total is obviously too high, because Alex has only $1.35 in his pocket. So clearly, fewer dimes are needed in the addition scenario. If a dime is taken away from the 10, then the number of nickels must be increased by 1—because Alex has 20 coins in his pocket. So, 9 dimes and 11 nickels add up to $1.45. This total is still greater than $1.35. So, try reducing the number of dimes in Alex’s pocket by 2. This would give him 8 dimes and 12 nickels (adding up to 20 coins), adding up to $1.40. This total is still too high, but we are getting closer to the goal of $1.35. So, let’s see what happens when the number of dimes in Alex’s pocket is reduced by 3 to a total of 7. This brings him to 7 dimes and 13 nickels, which adds up to $1.35.

  47.The Cat in the Hat. As you can see, the word cat is inserted in the word hat after the h. As you may know, the story revolves around a tall cat, who wears a red-and-white-striped hat and a red bow tie. It is a hilarious tale loved by children across generations.

  48.Edwin. The first three statements say the same thing—namely that Earl is the murderer. So, they are either all true or all false. They cannot be true, since there was only one true statement in the set. So, they are all false. We can now see that Edwin’s statement is true—Emma did indeed lie, as we just found out. This being the case identifies Edwin as the murderer—the only one who told the truth. Earl’s statement is obviously false but changes nothing.

  49.Second individual = Bawi, third individual = Mawi. The key is to translate “Duma” into English. The translation is “I am a Bawi.” Let’s break down why this is so. If the individual were a Bawi, he would claim to be one, since Bawis always tell the truth. So, in this case “Duma = I am a Bawi.” Now, if he were a member of the dishonest Mawi tribe, would he admit to it? Of course not. So, he would lie and say again “Duma = I am a Bawi,” but it would be a lie this time. Either way, “Duma = I am a Bawi.” The second individual clearly told the truth, while the third one lied. Finally, it is not possible to determine the tribe to which the first individual belonged.

  50.Here are the links: LASS—(1) mass—(2) mast—(3) malt—MALE.

  LEVEL 3: BRAINIAC

  51.The answer is 13. The box contains 24 shoes in total: 6 pairs of black shoes = 12 black shoes; 6 pairs of white shoes = 12 white shoes. Of the 24, half are right-foot-fitting and half are left-foot-fitting. In a worst-case scenario, we might pick all 12 left-foot-fitting shoes (of which 6 are black and 6 are white) or all 12 right-foot-fitting shoes (of which 6 are black and 6 are white). The 13th shoe drawn, however, will match one of these 12.

  52.27 full days, and on the 28th day the snail crawls out. Since the snail crawls up 3 feet, but slips back 2 feet, its net distance gain at the end of every day is, of course, 1 foot up from the day before. To put it another way, the snail’s climbing rate is 1 foot per day. So, on day two, the snail starts at 1 foot from the bottom. On day three, it starts at 2 feet from the bottom, and so on. Now, let’s project forward to day 27, where it starts at 26 feet from the bottom and 4 feet from the top. It goes up to 29 feet from the bottom and slides down 2 feet to 27 feet from the bottom. On the 28th day it starts at 27 feet from the bottom, goes up 3 feet, reaching the top, at which point it crawls out of the well. Game over. So, it took 27 full days and nights, and on the 28th day the snail crawled out.

  53.End is a car spin. It is mind-boggling to contemplate how a name might indeed harbor some prophetic message. Is it just coincidence? You decide.

  54.Thomas. As for the other puzzles in this genre, the final order reflects all the statements as follows (R = Rashad, M = Mary, J = Jack, W = Walter, T = Thomas): T—M—R—J—W.

  55.Believable.

  56.Astronaut.

  57.The child suggested deflating the tires, which lowered the height of the truck, allowing the driver to move it through.

  58.Right. (trip + chin + enough + sigh + temper = r + i + g + h + t = right.)

  59.59 socks. Counting a number of socks by 1s, 2s, 3s, and so on is the equivalent of dividing that numb
er into smaller groups of 1 sock, 2 socks, 3 socks, etc. So, to solve this puzzle, you must identify the number of socks between 50 and 60, which, when divided by 3, gives a remainder of 2 (equivalent to saying 2 socks left over), and when divided by 5, gives a remainder of 4. First, divide the numbers between 50 and 60 by 3, identifying those that leave a remainder of 2:

  50 ÷ 3 = 16, remainder = 2

  51 ÷ 3 = 17, no remainder

  52 ÷ 3 = 17, remainder = 1

  53 ÷ 3 = 17, remainder = 2

  54 ÷ 3 = 18, no remainder

  55 ÷ 3 = 18, remainder = 1

  56 ÷ 3 = 18, remainder = 2

  57 ÷ 3 = 19, no remainder

  58 ÷ 3 = 19, remainder = 1

  59 ÷ 3 = 19, remainder 2

  60 ÷ 3 = 20, no remainder

  You can now see that the only candidates between 50 and 60, which, when divided by 3 will leave a remainder of 2, are the numbers 50, 53, 56, and 59. Discard the others, proceeding to determine which of that group (50, 53, 56, or 59) will leave a remainder of 4 when it is divided by 5:

  50 ÷ 5 = 10, no remainder

  53 ÷ 5 = 10, remainder = 3

  56 ÷ 5 = 11, remainder = 1

  59 ÷ 5 = 11, remainder = 4

  As you can see, 59 socks is the answer. And, in fact, when you count 59 socks 3 at a time, you’ll get 2 left over; but when you count them 5 at a time, you’ll get 4 left over.

  60.All three men belonged to the liar clan. Tor’s answer, “Yes,” implies two possibilities. If Tor is a truth-teller, then his answer implies that Dor is also a truth-teller. If he is a liar, then “Yes” is an expected lie, and thus, so is his response that Dor is a truth-teller. Either way, Tor and Dor belong to the same clan. This is contrary to what Dor himself says. From this we deduce that Dor is a liar. So is Tor, also by deduction. We can now see that Gor lied when he implied that Dor is a truth-teller.

  61.E for eight. Each letter is the first one in the spelling of consecutive numbers: O (one), T (two), T (three), and so on.

  62.D for December. Each letter is the first one in the spelling of each month of the year in order of the 12-month calendar: J (January), F (February), M (March), and so on.

  63.W for words. Each letter is the first one in the spelling of each word in the saying, A picture is worth a thousand words.

  64.Independence Day, July 4, 1776. If you separate the digits as 7-4-1776, you will get the numerical version of the date on which the United States declared its independence from Britain.

  65.3 kilograms. If the brick weighs x, then ¾ x stands for ¾ its weight. Together with ¾ kilograms we get the balance with x kilograms. So, x = ¾ x + ¾, which means that x = 3.

  66.Charity—Clarity.

  67.10,080. The first number is multiplied by 2 (2 × 2 = 4), then each successive number is multiplied by a number that is one greater each time: 4 × 3 = 12, 12 × 4 = 48, 48 × 5 = 240, 240 × 6 = 1440, and finally 1440 × 7 = 10,080.

  68.The boy dressed in red dated the girl dressed in blue; the boy dressed in green dated the girl dressed in red; and the boy dressed in blue dated the girl dressed in green. You are told by one of the boys that no one had a date with a partner dressed in the same color: That is, the boy dressed in red did not have a date with the girl dressed in red; the boy dressed in green did not have a date with the girl dressed in green; and the boy dressed in blue did not have a date with the girl dressed in blue. The boy who made this observation was dressed in red, and he was not dancing with the girl dressed in green, since he made the observation to her and her partner. So, you can safely eliminate the girl in green as a possibility for the boy in red. This means the boy in red dated the girl in blue. Therefore, the boy dressed in green dated the girl dressed in red—since this is the only possibility left. The rest is straightforward.

  69.Stop. All the words are anagrams of each other.

  70.Gary. Alex and Tara clearly contradict each other, so one of their statements is true and the other false. Whichever is true, we have now identified that the remaining statements must be false, meaning that Daniela and Gary lied. From this, we can see that Gary, contrary to what he said, is our robber.

  71.34 + 43 – 6 = 71.

  72.72 ÷ 8 = 7 + 2.

  73.Liver—Lover.

  74.Sender—Tender.

  75.Rhonda = violinist, Bernard = drummer, Peter = singer, Selena = pianist. We can eliminate Peter as the violinist because we know he attended many of the pianist’s concerts with the violinist. Selena and Bernard can be eliminated, as well, since they often play with the violinist. So, that leaves Rhonda as the violinist. We are told Peter is not the drummer, and again, he has attended the pianist’s concerts, so by deduction Peter is the singer. Then Selena is not the drummer because we are told that the drummer often performs with her. She is also not the violinist (Rhonda is) nor the singer (Peter is). So, by elimination she must be the pianist. This leaves the drummer as the only possibility left for Bernard.

  LEVEL 4: MASTERMIND

  76.2 revolutions. Many people come up with an incorrect solution to this puzzle. Since the circumferences of the two coins are equal, and since the circumference of A is laid out once along that of B, they argue that A must make one revolution about its own center. However, if you actually carry out the instructions of this puzzle with, for example, two quarters, you will find that the outer quarter will make two complete revolutions, not one. The mathematical explanation of this apparent paradox can be found in an analysis of the figure known as a cycloid—this is defined as a curve tracing the path traversed by a point on the circumference of a wheel as it rolls without slipping upon a straight line. The cycloid was studied and named by Italian physicist and astronomer Galileo in 1599.

  77.25 rungs. At the beginning, we do not know what rung the firefighter is standing on, except that it is the “middle” rung. So, let’s label her starting rung as 0, that is, consider the middle rung to be analogous to the 0, or ground level, of a building. Each rung above and below 0 can then be compared to a level above or below this ground level. Obviously, since it is the middle rung, there will be as many rungs above it as there are below it. You are first told that the firefighter went up 3 rungs from the 0 rung. You are then informed that she stepped down 5 rungs. So, from rung 3 above 0, she went down 5 rungs, ending up at 2 rungs below the 0 point (which you can also represent as -2). Next, the puzzle tells you that the firefighter climbed up 7 rungs (from rung -2). So, she started from rung -2 and went up 7 rungs from there. This means she ended up at rung 5 above the starting point or 0 rung. Finally, the puzzle tells you that the firefighter climbed up another 7 rungs (from rung 5 above) to the roof. This means that she continued climbing (from rung 5 above), moving up another 7 rungs, to rung 12 beyond her starting point. Rung 12 above is the top part of the ladder, because from that rung the firefighter stepped onto the roof. Now, let’s complete the ladder. You know that it has 12 rungs above the 0 rung. Since the 0 rung is the middle rung, a complete ladder will, of course, also have 12 rungs below the zero rung. Therefore, the ladder consists of 12 rungs above the 0 rung, 12 below it, and the 0 rung itself. This makes, of course, 25 rungs in total.

  78.Jerry. As with the other puzzles in this genre (7, 32, 54), this final order reflects all the statements as follows (J = Jerry, B = Bob, P = Paula, S = Sarah, T = Tim, L = Lorraine): J—B—P—S—T—L.

  79.33. 33 × 3 = 99 ÷ 9 = 11.

  80.17. 17 + 2 = 19; 17 × 3 = 51 - 17 = 34.

  81.Six draws. The reasoning is always the same. Assuming the worst-case scenario, you will draw out five balls of different colors—a white, a black, a green, a blue, and a yellow, in no particular order. Now, whichever ball you draw out next (remember that there are still balls of each color left inside in the box), it will match one of the five that have been drawn out. This is the sixth draw. If it is a white ball (from inside the box), it matches the white ball outside; if it is a black ball, it matches the black ball outside; and so on.

  82.Eight draws. Nothing
changes in the reasoning. Assuming the worst-case scenario, you will draw out seven balls of different colors—a white, a black, a green, a blue, a yellow, a brown, and the single red one, in no particular order. Now, whichever ball you draw out next (remember that there are still balls of each color in the box except for red), it will match one of the balls that have already been drawn out, except, of course, the red one—white, black, green, blue, yellow, or brown. That constitutes the eighth draw. If you draw a white ball (from inside the box), it matches the white ball outside; if it is a black ball, it matches the black ball outside; and so on.

  83.123. 123 × 2 = 246 – 1 = 245.

  84.13. 13 × 4 = 52. Note the sum of the digits in “13” is “4.”

  85.3. The steps break down as follows:

  3 + 4 = 7 (“Add me to the next number above me.”)

  7 x 3 = 21 (“Multiply the result by me …”)

  21 + 3 = 24 (“… and add me again.”)

  2 + 4 = 6 (“Add the digits in the result.”)

  6 ÷ 2 = 3 (Divide in half for the final answer.)

  86.Wife. The woman has a sister, since she uses the expression “my sister’s.” Her sister’s nephew in this case is obviously the woman’s son. Think of it this way. Suppose you have a sister and you have a son. Who is the son in relation to your sister? Her nephew, of course. The puzzle also says that her nephew is the son of the man in the photo. Conclusion? The woman is looking at a photo of her husband.

  87.Aunt. Mary’s mother is also her sister’s mother, needless to say. So, the mother’s grandson can only be her sister’s son, since Mary has no children. This means that the grandson is her nephew and she is his aunt.