7  3    8  8    5  0    6  ?

6  3    4  2    6  4    9  5

Answer hermes

2.

2  7    0  3    0  11    2  ?

8  9    5  6   10  11    4  3

Answer

HELLO, GOODBYE!

3. 12 members were present at a board meeting. Each member shook hands with all of the other members before & after the meeting. How many hand shakes were there?

Answer132. Think of it this way: the first person shakes hands with 11 people, the second person also shakes hands with 11 people, but you only count 10, because the hand shake with the first person was already counted. Then add 9 for the third person, 8 for the fourth, & so on. 66 hand shakes took place before & after the meeting, for a total of 132.

PROBABILITY UNIVERSITY

4. At Probability University, there are 375 freshmen, 293 sophomores, 187 juniors, & 126 seniors. One student will randomly be chosen to receive an award. What percent chance is there that it will be a junior? Round to the nearest whole percent.

Answer19%. This puzzle was easy. Divide the number of juniors (187) by the total number of students (981), & then multiply the number by 100 to convert to a percentage.

A DOZEN EDGES

5. If you take a marker & start from a corner on a cube, what is the maximum number of edges you can trace across if you never trace across the same edge twice, never remove the marker from the cube, & never trace anywhere on the cube, except for the corners & edges?

Answer9. To verify this, you can make a drawing of a cube, & number each of its 12 edges. Then, always starting from 1 corner & 1 edge, you can determine all of the possible paths for tracing along the edges of a cube. There is no need to start from other corners or edges of the cube, as you will only be repeating the same paths. The process is a little more involved than this, but is useful for solving many types of spatial and logical puzzles.

TWO & THREE

6. A cube is made of a white material, but the exterior is painted black. If the cube is cut into 125 smaller cubes of exactly the same size, how many of the cubes will have 2 of their sides painted black?

Answer44. 36 of the cubes have EXACTLY 2 of their sides painted black, but because a cube with 3 of its sides painted black has 2 of its sides painted black, you must also include the corner cubes. This was a trick question, but hopefully the title of the puzzle tipped you off to this.

FOLD IN HALF

7. If you started a business in which you earned $1 on the first day, $3 on the second day, $5 on the third day, $7 on the fourth day, & so on, how much would you have earned with this business after 50 years (assuming there are exactly 365 days in every year)?

Answer$333,062,500. To begin with, you want to know the total number of days: 365 x 50 = 18250. By experimentation, the following formula can be discovered, & used to determine the amount earned for any particular day: 1 + 2(x-1), with x being the number of the day. The title again holds a hint, although this 1 may have been a bit more obscure. Take half of the 18250 days, & pair them up with the other half in the following way: day 1 with day 18250, day 2 with day 18249, & so on, & you will see that if you add these pairs together, they always equal $36500. Multiply this number by the total number of pairs (9125), & you have the amount you would have earned in 50 years. Except for math gurus (I'm not 1), this puzzle may have proved to be tough. Someone pointed out that a much easier method for solving this problem is squaring the total number of days worked - I like doing things the hard way, though.

PAY RAISE/PAY CUT

8. A worker earns a 5% raise. A year later, the worker receives a 2.5% cut in pay, & now her salary is $22702.68. What was her salary to begin with?

Answer$22176.

9. Two trains, each two miles long, enter two one mile long tunnels that are two miles apart from one another on the same track. The trains enter the tunnels at exactly the same time. The first train is going 5 miles/hour, and the second train is going 10 miles/hour. What is the sum of the lengths of the two trains that will protrude from the tunnels at the exact moment that they collide, assuming that neither train changes its speed prior to collision? The trains are on the same track headed in opposite directions (i.e. directly toward one another).

Answer2 2/3 miles. The trains are exactly 4 miles apart. Their combined speed is 15 miles/hour, so it will take them 16 minutes to collide. The first train will have travelled 1 1/3 miles, so 1/3 mile of it will be out of the tunnel in front, & 2/3 mile of it will be out in the back on collision. The other mile of it will be in the tunnel. The second train will have travelled 2 2/3 miles, so only 1/3 mile of it will still be in the tunnel, so 1 2/3 miles of it will be out of the tunnel.

10. If the same functions are applied to reach the results in each of the three sets of numbers, find what number should replace the ? in the last set:

21  5        28  13        16 2

  24           30            ?

17  7        25  7         10 8

Answer30. In each set, the difference between the two leftmost numbers is divided by two, and then multiplied by the sum of the two rightmost numbers. The product is written in the middle for each set.

11. You have 1,432 feet of fence that must be strung out in a straight line. A fence post must be placed for every 4 feet of fence, so how many fence posts will be needed?

Answer359. If you answered 358, you must remember that the fence must begin & end with a post, & dividing 1,432 by 4 leaves one end without a post.

12. If each letter in the following equations represents a number from 1 through 9, determine what number each letter represents.

A. A+A+B+C = 13

B. A+B+C+D = 14

C. B+B+C+D = 13

AnswerA=3, B=2, C=5, and D=4. An alternate answer is A=2, B=1, C=8, and D=3, which was found by Jill (no last name specified) & by Sharon Kienzle. Ms. Kienzle also found A=4, B=3, C=2, & D=5.

13. Anyone telesent (like being teleported or "beamed up") to Space Station Exray will arrive in pod A, B, or C. You are twice as likely to arrive in pod A than in pod B, & three times as likely to arrive in pod B than pod C. How likely is it that you will arrive in pods B, C, & A, in that order, the only three times that you are telesent to Space Station Exray? You may express your answer as a fraction or as a percentage.

AnswerThe answer is 9/500, or 1.8%. The problem can be set up algebraically. For each trip, there is a 100% chance that you will arrive in pod A, B, or C. Let X be the chance that you arrive in pod A, & since it is twice as likely that you will arrive in A than B, there is only half the chance that you will arrive in B than A. So B is 1/2 X. By the same reasoning, there is only 1/6 the chance you would arrive in C than A, so C is 1/6 X. The equation thus looks like this: 100 = X + 1/2X + 1/6X. X=60, so A = 60, B = 30, & C = 10. These numbers correspond to the % chances you would arrive in each pod.

The answer is found by multiplying these three percentages together (i.e. .3 x .1 x .6). There is only a 1.8% chance that you would arrive in these 3 pods in this particular order for your only 3 trips to Exray.

14. In a perfectly circular arena, I walk from the edge directly to the center. I then turn directly to my left, & walk in a straight line to the edge of the arena. I then turn to the right & follow along the edge for a total of 500 meters until I arrive at the point that I started from. What is the circumference of the inner edge of the arena?

Answer666 2/3 meters. Draw a diagram of the route I took, and then think of it in terms of a pie chart. I walked exactly 3/4 of the way around the arena, so simply multiply the 500 meters I walked by 4/3 to get the answer.

15. If 7 web programmers can format 1001 puzzles in 429 minutes, how long does it take 3 web programmers to format those 1001 puzzles?

Answer1001 minutes. The total amount of work is 7 times 429 programmer-minutes, so 3003 programmer-minutes. So 3 programmers will need 3003/3 = 1001 minutes.

16. If you have 3 dice that are shaped as a tetrahedron, a cube, & an icosahedron, & you rolled each of them, each die would display a number from 1-4, 1-6, & 1-20, respectively. Assume that the tetrahedron & icosahedron are regular. If there is an equal chance that a die will display any of its numbers each time it is rolled, what percent chance is there that the numbers rolled will total 7 if all three dice are rolled once, & the numbers they display are added together?

Answer14/480, 7/240, or approximately 2.91%, as there are 14 situations where the dice will show a total of 7 out of 480 possible combinations.

17. What are the maximum of separate volumes that can be formed by 2 interpenetrating cubes?

a) Use only the surfaces of the cubes for consideration of the bounded volumes.

b) Do not consider any subdivisions of the volumes.

AnswerTwelve.

18. Andy, Bart, and Chris are eating at Smiley's All You Can Eat Pizza Buffet. Andy made 2.4 times as many trips to the buffet as Bart, and Bart made 6 fewer trips than Chris. What is the smallest possible total number of trips the 3 made to the buffet, assuming that each person made at least one trip?

AnswerThere were 28 total trips made, with Andy making 12 of them, Bart making 5, and Chris making 11. The puzzle can be expressed algebraically as A + B + C = X, where X is the total number of trips. A = 2.4B. Because A has to be a whole number (Andy couldn't make 2.4 trips, for example), you quickly find that 12 and 5 are the lowest possible whole numbers for A and B, which makes C 11.

CURRENT EVENT

19. In training for a competition, you find that swimming downstream (with the current) in a river, you can swim 2 miles in 40 minutes, & upstream (against the current), you can swim 2 miles in 60 minutes. How long would it take you to swim a mile in still water?

AnswerYou are able to swim downstream at 3 miles an hour, & upstream at 2 miles an hour. There is a difference of 1 mile an hour, which is the river helping you in 1 direction, & slowing you in the other direction. Average the 2 rates, & you have the rate that you can swim in still water, which is 2.5 miles an hour. You can thus swim a mile in still water in 24 minutes.

BUSINESS PSYCHOLOGY

20. All of the students at a college are majoring in psychology, business, or both. 73% of the students are psychology majors, & 62% are business majors. If there are 200 students, how many of them are majoring in both psychology & business?

AnswerIf 73% of the students are psychology majors, we know that 27% are not psychology majors. By the same reasoning, 38% are not business majors, because 62% of the students do major in business. So:

27 + 38 = 65

65% of the students are not majoring in both psychology & business, so 35% are double majors, a total of 70 students.