$ THE MISSING DOLLAR RIDDLE $ Three friends check into a motel for the night and the clerk tells them the bill is $30, payable in advance. So, they each pay the clerk $10 and go to their room. A few minutes later, the clerk realizes he has made an error and overcharged the trio by $5. He asks the bellhop to return $5 to the 3 friends who had just checked in. The bellhop sees this as an opportunity to make $2 as he reasons that the three friends would have a tough time dividing $5 evenly among them; so he decides to tell them that the clerk made a mistake of only $3, giving a dollar back to each of the friends. He pockets the leftover $2 and goes home for the day! Now, each of the three friends gets a dollar back, thus they each paid $9 for the room which is a total of $27 for the night. We know the bellhop pocketed $2 and adding that to the $27, you get $29, not $30 which was originally spent. Where did the other dollar go????:
The facts in this riddle are clear: There is an initial $30 charge. It should have been $25, so $5 must be returned and accounted for. $3 is given to the 3 friends, $2 is kept by the bellhop - there you have the $5. The trick to this riddle is that the addition and subtraction are done at the wrong times to misdirect your thinking - and quite successfully for most. Each of the 3 friends did indeed pay $9, not $10, and as far as the friends are concerned, they paid $27 for the night. But we know that the clerk will tell us that they were charged only $25 and when you add the $3 returned with the $2 kept by the bellhop, you come up with $30.

Take the number of your fingers multiplied by the number of you toes divided by one half and add it to the number of months in a year. What is the total?:
10x10=100÷1/2=200+12=212 *NOTE: For another way to look at this - Stuart writes: I noticed that the corresponding answer to puzzle 1 says "10x10=100÷1/2=200+12=212", when in fact it should be "8x10=80÷1/2=160+12=172" as you have 8 fingers and 2 thumbs!

A mother and father have six sons and each son has one sister. How many people are in that family?:
9

Jenn has half the Beanie Babies that Mollie has. Allison has 3 times as many as Jenn. Together they have 72. How many Beanie Babies does each girl have?:
If Mollie has twice as many Beanie Babies as Jenn and Allison has 3 times as many as Jenn, then the total of 72 must be divided by 6. 72÷6=12. Therefore: Jenn has 12 Beanie Babies, Mollie has 24 Beanie Babies, and Allison has 36 Beanie Babies.

Kevin is 14 inches taller than George. The difference between Kevin and Richard is two inches less than between Richard and George. Kevin at 6'6" is the tallest. How tall are Richard and George ?:
If Kevin is 6'6" tall, George must be 5'4" tall, and Richard must be 6' tall because he is 6" shorter than Kevin and 8" tall than George.

A baseball team had just won the championship game and the players wanted to congratulate each other. They began shaking hands, but each player only shook hands with every other player just once. There are, of course, only 9 players on a baseball team. How many times did the players shake hands?:
The first player only shakes hands with 8 other players, the second player only shakes hands with 7 other players ( he already shook hands with the first player!), the third player only shakes hands with 6 players ( he already shook hands with the first player and second player ), and so on, until the last player who only has one possibility left. Therefore: 8+7+6+5+4+3+2+1=36

A jar has 4 amoebas in it to start. Amoebas split their cells in two ( therefore doubling in size) once every minute. The jar will be completely filled in 10 minutes. How long would it take to fill the same sized jar if had 8 amoebas in it to start?:
9 minutes

There are 100 golfers in the local match play contest. If a player loses a match, he is immediately eliminated from the contest. How many matches will be played to determine the winner?:
(a)If there is to be only one winner, than there are 99 loses, therefore there were 99 matches. You can also do this with math: in round 1 there would be 50 matches to produce 50 winners, round 2 would have 25 matches to produce 25 winners, round 3 would have 12 matches to produce 12 winners ( one person of the 25 winners would have to wait until later to play again ), round 4 would have 6 matches to produce 6 winners, round 5 would have 3 matches to produce 3 winners, round 6 would have 2 matches ( the player left out before would now play to make it an even field ) to produce 2 winners, these 2 would play for the championship. So: 50+25+12+6+3+2+1=99 (b)We received an alternate solution to the above answer that we think is a well thought out solution; it eliminates having 1 person waiting to play at a later time: The first round is 50 matches eliminating 50 golfers, the second is 25 matches eliminating 25 golfers. For the third round the remaining 25 are divided into pools of 5 at random and face two matches each (each vs. a different randomly selected opponent in the pool). I think you will find that there will be two golfers and two only from each pool who will be dual winners. They will advance. The third round was then 5 pools of 5 matches so 25 more matches (100 total so far). The fourth round will be 5 matches eliminating 5 golfers. These five participate in a pool (fifth round) just like the third round (5 more matches and 2 emerge). The two play the championship match. So by round the matches are: 50+25+25+5+5+1 = 111 matches

Two trains are on a head on collision course. The trains are currently 65 miles apart. The north bound train is traveling at 55 miles per hour and the south bound train is traveling at 80 miles per hour. What is the distance between the trains two minutes before they collide?:
If the trains are moving toward each other we combine their speeds to give us their speed basis. So: 55+80=135mph. Divide this speed by 60 minutes to give the speed they are traveling each minute=2.25 miles/minute. Therefore: 2 minutes before impact they are 4.5 miles apart.

A car travels at a speed of 30 mph over a certain distance, and then returns over the same distance at a speed of 20 mph. What is the average speed for the total trip?:
24 mph. Most people are quick to answer 25 mph, but this is not correct, as we will see. Let the distance traveled be 60 miles each way. Then, the trip out = 60/30 = 2 hours, and the trip back = 60/20 = 3 hours. Therefore: the 120 mile trip = 120/5 = 24 mph.

A woman has 100 yards of cloth on a single roll, and she wants to divide it into 100 lengths of 1 yard each. It takes her 3 seconds to cut each length. Working non-stop, how long will it take her to cut all 100 pieces?:
The answer is 297 seconds, not 300 as most people would suppose. This is because the 100 pieces are made in 99 cuts. The last cut made results in 2 pieces instead of only one piece.

Find a simple method of solving: 6751X + 3249Y = 26751 3249X + 6751Y = 23249:
Add the equation to give: 10000X + 10000Y = 50000 Divide by 10000 to give: X + Y = 5 Subtract to give: 3502X - 3502Y = 3502 Divide by 3502 to give: X - Y = 1 Therefore: X = 3 and Y = 2

Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 18 MPH between the 2 friends until the friends meet. How far does the pigeon travel?:
It takes 3 hours for the friends to meet; so the pigeon flies for 3 hours at 18 MPH=54 miles.

Nick and John were exercising when the subject of weight came up. Nick had no problem telling John his weight, but John said he had more "mass" than he wanted. He wouldn't come right out and reveal his weight; so he told Nick this riddle. " I weigh 147 pounds plus half of my weight," he said. How much does he weigh?:
If John weighs 147 pounds plus half of his body weight, the 147 pounds represents the other half. John weighs 294 pounds.

A farmer knows that 20 of his hens, housed in 3 coops, will hatch 30 eggs in 18 days. How long will it take 30 hens, housed in 4 coops to hatch the same number of eggs?:
You can't shorten the process of egg-hatching by increasing the number of chickens. Therefore, 30 hens will also need 18 days to hatch their eggs.

How can you measure 1 gallon of juice out of a barrel, if all you have available is a 3-gallon and a 5-gallon pitcher?:
Fill the 3 gallon pitcher and pour it into the 5 gallon pitcher. Now fill the 3 gallon pitcher again and fill the 5 gallon pitcher to capacity. What remains in the 3 gallon pitcher is one gallon of juice.

Students at Monty High with a class size under of 30 took a math test. One third of the class got a "B", one quarter a "B-", one sixth a "C", and one eighth failed. The remainder of the students got an "A" How many students got an "A"?:
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First find the common denominator for the numbers 3, 4, 6, and 8. The only common denominator less than 30 is 24. Therefore, the students with a "B" = 8, "B-" = 6, "C" =4, failed = 3. This represents 21 of the students; so the 3 remaining students received an "A".

When manufacturing bars of soap, the cutting machine produces scraps. The scraps from 11 bars of soap can be made into one extra bar. What is the total number of bars that can be made after cutting 250 bars of soap?:
Divide 250 by 11 which equals 22.8. Now when you combine the extra 8 scraps with the scraps you'll have from the 22 bars, you'll have 30 more scraps. They will produce 2 more bars; so the total additional bars will be 24.

Kerry loves dumplings. He can eat 32 of them in an hour. His brother Pete needs 3 hours to eat the same amount. How long will it take them both together to eat 32 dumplings?:
If Kerry eats 3 times as fast as Pete, he must be able to eat 3 times as many dumplings as his brother. Therefore, Kerry eats 24 while Pete eats 8 ( 32 ÷ 4 = 8 ). Together it takes them 45 minutes.

Joe bought a bag of oranges on Monday, and ate a third of them. On Tuesday he ate half of the remaining oranges. On Wednesday he looked in the bag to find he only had two oranges left. How many oranges were originally in the bag?:
He had 6 oranges to start with, and ate 2 the first day and 2 the second day.

Joan and Jane are sisters. Jean is Joan's daughter and 12 years younger than her aunt. Joan is twice as old as Jean. Four years ago, Joan was the same age as Jane is now, and Jane was twice as old as her niece. How old is Jean?:
Joan is 32, Jane is 28, and Jean is 16.

Because cigars cannot be entirely smoked, a hobo who collects cigar butts can make a cigar to smoke out of every 5 butts that he finds. Today, he has collected 25 cigar butts. How many cigars will he be able to smoke?:
6, he makes 5 originals from the 25 butts he found, and after he smokes them he has 5 butts left for another cigar.

What row of numbers comes next? This is a tough one! 1 11 21 1211 111221 312211 13112221:
The next row is 1113213211 Starting with the second line, every line describes the line before it. In writing, it is: One One Two Ones One Two One One etc. etc.

What is the largest possible number you can write using only 2 digits - just 2 digits, nothing else?:
99, this is 9x9x9x9x9x9x9x9x9 or 387,420,489.

A carpenter was in a terrible hurry. He had to work as quickly as possible to cut a very heavy 10 foot plank into 10 equal sections. If it takes 1 minute per cut, how 'long' will it take him to get the 10 equal pieces?:
9 minutes. It only takes 9 cuts to get 10 equal sections.

In your sock drawer, you have a ratio of 5 pairs of blue socks, 4 pairs of brown socks, and 6 pairs of black socks. In complete darkness, how many socks would you need to pull out to get a matching pair of the same color?:
4. If you don't agree, try it yourself!

A carpenter was in a terrible hurry. He had to work as quickly as possible to cut a very heavy 10 foot plank into 10 equal sections. If it takes 1 minute per cut, how many cuts will it take him to get the 10 equal pieces?:
in just 5 cuts. The first cuts down the middle and the rest width ways.

Take 12 toothpicks, pencils, or q-tips. Now subtract one, Now you should have 9 in front of you. Did you do it right?:
Technically you have 11 toothpicks left over right? 12 - 1 = 11
But if you arrange them into letters, You will have 11 toothpcks that spell out the Word NINE !!