PROMOTIONAL MAILER: LOGIC PUZZLES
In late 2004, Clym Environmental sent out a number of promotional mailers to members of the Life Sciences industry. Included with this mailer were a number of "logic puzzles".
If you'd like to learn more about the mailer (and puzzles), or to be included in future mailings, please contact us.
Below you will find the answers to all 75 logic puzzles...
- The grid should contain one 1, two 2s, three 3s, four 4s, five 5s, six 6s, seven 7s, and eight 8s. Therefore, the missing numbers are 7, 7, 8, 2. All the numbers are placed so that two identical numbers are never adjacent.
- D. Each pair of circles produces the circle above by carrying on elements that they have in common. Different elements disappear.
- 4. In the first pentagon 5 x 5 x 125 = 3125 or 55; in the second pentagon, 3 x 9 x 9 243 or 35; in the same way, 16 x 8 x 8 = 1024 or 45.
- A D G H F B E C
- 1) In the first bar, 7 x 4 x 8 x 8 x 2 = 3584. Similarly, 3 x 5 x 8 x 4 = 480. Following the same formula, the missing number in the second bar is 2268 and, in the third, 2688 and 768.
2) In the first bar, 58 x 2 = 116. In the same vein, 16 x 1 = 16. Using the same formula, the missing number in the second bar is 657 and, in the third, 162 and 72.
- 49 meters. A=9m B=8m C=8m D=6m E=6m F=4m G=4m H=2m I=2m Total=49m
- Two segments; all triangles do not need to be the same size.
- E. The two figures merge into one by superimposing one onto the other, except that when two lines appear in the same position they disappear.
- 44. 28 huskies with four legs each plus 44 penguins with two each, making 200 legs in all.
- She lives on the 27th floor. The elevator came down from the 36th to the 28th floor - 9 floors; or it came up from the first to the 27th floor. Therefor there is a 3:1 chance of it going up rather than down.
- Mark four points exactly opposite of each of the four people. Now count the number of points that lie between each pair. The place to sit is midway between the points. This principle works for any seating plan.
- The dalmations are called Andy (owned by Bill) and Donald (owned by Colin).
- Anastasia tells a lie when she says that the number is below 500. The only square and cube between 99 and 999 whose first and last digit is 5, 7, or 9 is 729.
- C. The middle pattern is removed and encases the outer pattern of the original figure.
- Arrange them into groups of three, each totaling 1000.
457 + 168 + 375 = 1000
532 + 217 + 251 = 1000
349 + 218 + 433 = 1000
713 + 106 + 181 = 1000
- D. The small circle moves forward tow and one back. The medium-sized circle moves one back and two forward. The large circle moves forward one and two back.
- 20. Start at 10 and jump to alternate segments, adding 1, then 2, then 3 and so on.
- Strong, weak, strong. He will always beat the weak player, so playing this way gives him two chances to beat the strong one.
- B. The figures are flipped vertically.
- 24. In the first circle, 56 + 79 divided by 5 = 27. The same formula applies to circles two and three.
- The number of squares on the card is immaterial. The odds are always 2:1 against.
- 135-7531. Turn the page upside down and read off the spaces between the tiles.
- Major Mustard. Tabulate the results so that each set equals 71. There are only three possible ways to do this: 25, 20, 20, 3, 2, 1; 25, 20, 10, 10, 5, 1; and 50, 10, 5, 3, 2, 1. The first set is Colonel Ketchup's (since 22 cannot be scored in two shots in the other sets); the third set is Major Mustard's (as we know that he scores 3). So Major Mustard hit the bull's eye.
- 7²=49. The 6 has been flipped to turn it into a 9 and the 2 becomes a square.
- I am forty and my daughter is ten.
- Graham is 9 years old and Frederick is 27. Thus, 27 squared is the same as 9 cubed; 729. There are 18 steps, 36 pickets, and 243 bricks, which, when added together, give the house number of 297.
- Divide the central number by 5 to give the top number. Add the digits of the central number to give the bottom left number. Reverse the digits of the central number and divide by three to give the bottom right number.
- B. It is a straight-sided figure within a curved figure. The rest are curved figures within a straigh-sided one.
- 36: 21 blue, 1 black, and 14 striped.
- 450 meters
- 33. Multiply diagonally opposite squares and subtract the smaller product from the larger: (13 x 5) - (8 x 4) = 33.
- Mr. and Mrs. Chester.
- Hold the book up to a mirror. You will see that the numbers 1, 2, 3, 4, 5 appear in sequence.
- 11 + 12 + 1 + 2 = 26
10 + 3 + 9 + 4 = 26
5 + 6 + 7 + 8 = 26
- 252. Each number represents the number of possible routes to each intersection.
- Three chances in four. Look at the possible combinations of drawing balls: black-black; white-black; black-white; and white-white. The only one of the four possible combinations in which drawing a black ball does not occur is the fourth one. The chances of drawing at least one black ball are, therefor, three in four.
- E. In all the others, if the line dividing the square creates a mirror image, the correct mirror image has been shown.
- So that:
1) No two consecutive numbers appear in any horizontal, vertical, or diagonal line;
2) No two consecutive numbers appear in adjacent squares.
- Ernie Black
- 22 ½ miles. Work out how long it takes Russell Carter to walk home. Spot has been running all this time at his given constant speed so it is simple to work out how many miles Spot has covered during this period. Russell walks for 10 miles at 4 mph, taking 2 ½ hours. Spot is running for 2 ½ hours too, at 9 mph, which means he covers 22 ½ miles.
- C. B and D, and A and E are the same, with large and small circles reversed.
- A. There are six triangles, each with its base on one of the sides of the hexagon. Each triangle increases in height by a quarter of the width of the hexagon at each stage.
- D. The smallest number is dropped each time and the remaining numbers appear in reverse order.
- C. The square turns 90° clockwise at each stage. Similarly, the shading also moves one segment clockwise at each stage.
- 90. You can buy nine tickets from each of the ten stations: 9 x 10 = 90.
- A. The figures change places so that the one in front goes to the back and vice versa.
- 60°. If a third face diagonal, BC, is drawn, this completes an equilateral triangle. All its sides are equal because they are cube diagonals. Being equilateral, all its angles are 60°.
- 2519 prisoners
2519 divided by 3 = 839 tables with 2 leftover
2519 divided by 5 = 503 tables with 4 leftover
2519 divided by 7 = 359 with 6 leftover
2519 divided by 9 = 279 with 8 leftover
2519 divided by 11 = 229 exactly
- I forgot to mention that my clock was digital. One line was not functioning on the eight lines that make up each digit.
- D. The three squares form four triangles.
- Alf Muggins. If it was Jack Vicious, the statements of Alf Muggins and Jim Pouncer would be true. If it was Sid Shifty, the statements of Jack Vicious, Alf Muggins and Jim Pouncer would be true. If it was Jim Pouncer, the statements of Sid Shifty and Alf Muggins would be true. Therefore it is Alf Muggins, and only the statment of Jim Pouncer is true.
- Spencer prunes six more trees than Don.
- If the shorter pieces, placed end to end, are longer than the largest piece, then they will form a triangle.
- No in both cases, except if the 6 is turned upside down into a 9. If the numbers were 1, 4, 7, and 9, it would never be divisible by 9 but always by 3.
- 1:5. There are six possible pairings of the four balls:
2. Red no. 1/white
3. Red no. 1/black
4. Red no. 2/white
5. Red no. 2/black
The black/white combination has not been drawn. This leaves five possible combinations. Therefore the chances that the red/red pairing has been drawn are 1:5.
- Mr. Carter is the driver.
- 12. Add the digits in the first block (9 + 9 + 7 + 2) and you get the next number, 27. Add the digits in the second block and you get 18. Add the digits in the third block and you get 21. Add the digits in the fourth block (3 + 6 + 2 + 1) and you get the answer, 12.
- 18 days. If it takes a man 27 days to drink one barrel, he drinks 0.037 of a barrel each day. Similarly, a woman drinks 0.0185 of a barrel each day. Added together, a day's combined drinking consumes 0.0555 of a barrel. In this case, to drink the whole barrel takes 18.018 days.
- Any valley on or near the equator, owing to the revolution of the earth.
- By lifting the water tank onto its near-side edge. If you cannot see the far edge then the tank is more than half full. If you can just see the far edge then the tank is exactly half full. If you can see below the far edge then the tank is less than half full.
- E. A is a mirror image of C; B is a mirror image of D.
- The census-taker should have known the number of the house, as he could see it. But he did not know their ages, therefore the house must be number 14. He needed more information to decide whether their ages were 6, 6, 2 or 8, 3, 3. When the woman says "eldest" daughter, he knows they were 8, 3, and 3.
- Let us assume that 240 fingers could be 20 aliens with 12 fingers each or 12 aliens with 20 fingers each, etc. This does not provide a unique answer and so eliminates all numbers that can be factorized.
Now consider prime numbers: There could be one alien with 229 fingers (not allowed, according to sentence one) or 229 aliens with one finger (not according to sentence two). There could be 41 aliens with 7 fingers or 7 aliens with 41 fingers. Again, this does not proivde a unique answer and so eliminates all prime numbers except those squared. There is only one of these between 200 and 300 and that is 289 (17²). There are 17 aliens with 17 fingers in the room.
- The first man places a $1 bill on the counter. The second man puts down three quarters, two dimes and a nickel - amounting to one dollar. Had he wanted a 90-cent beer, he had the change to offer the exact amount.
- 2. If all 49 women wore glasses then 21 men wore glasses too. If 11 of these men were uner 20 years of age, only 10 men older than 20 years of age wore glasses. Then 10 - 8 = 2 men is the minimum number.
- At first glance the best option seems to be the first. However, the second option works out best.
- 8679. Turn the card upside down and add the two numbers.
- "Push" on one side; "Pull" on the other side.
- No. The pigeons remain at 200 lbs even while flying. Those flying up would reduce the weight, but those flying down would increase the weight, so balancing the total weight.
- Edward Peters; Robert Edwards; Peter Roberts. Mr. Peters must be Edward because the man who spoke last is Robert, and he is not Mr. Peters.
- Charlie puts the handkerchief under a door and stands on the corner at the other side.