Misc Puzzles 1

Q1.  
You are given 5 bags. There are 10 beads in each of the bags. In four of the bags, the beads each weigh 10 grams.  In the remaining bag,  each bead  weighs only 9 grams. All the bags and beads look identical. You must  find out which bag has the lighter beads. The problem is that all the bags look identical and all the beads look identical. You can use a scale, but it has to be a single-tray scale, not a two-tray balance scale.  Also, you may use the scale only once. How can you find out which bag has the lighter beads? 

Q2.
Now you should be able to solve this variation, no problem:
You have 10 bags of gold coins, 10 coins per bag, 10 grams per coin, but one bag of coins weigh only 9 grams per coin (because of low quality). How do you find out which bag contains low quality gold coins?  You may use a scale only one time.  Thanks to Jason Vuong for this variation!

Q3. 
You have 9 marbles:  8 of them weigh 1 ounce each; 1 weighs 1.1 ounce. The 9 marbles are all uniform in size, appearance and shape.  You have access to a balance scale containing 2 trays - you may use the balance 2 times.  You must determine which of the 9 marbles is the heavier one using the balance only 2 times.






Ans1. Label the bags from 1 to 5. Take 1 bead out of Bag 1, and label it 1. Take 2 beads out of Bag 2, and label them both with a 2. Take 3 beads out of Bag 3, and label each with a 3. Continue this pattern with Bags 4 and 5. Put these 15 beads on the tray of the scale.
If all 15 weighed 10 grams, the scale would register 150 grams. But since one or more of the beads weighs only 9 grams, the scale will register less than 150. Subtract the number on the scale from 150. Your answer will tell you the number of the bag with the lighter beads. (If the scale registers 148, it’s bag #2. If the scale registers 145, it’s bag #5.) 

Ans2.
step 1: we name all the bag of gold coins as #1, #2, #3......#8, #9, and #10
step 2: we put 1 coin from bag #1, 2 coins from bag #2, 3 coins from bag #3.........8 coins from bag #8, 9 coins from bag #9, and 10 coins from bag 10 onto the scale. Find out the total weight.
step 3: the total weight should have been 10 grams X
(1+2+3+4+5+6+7+8+9+10=55) = 550 grams if all coins are the same (10grams each).
step 4: Subtract the total of step 2 from total of step 3.
Conclusion: If step 4 results 1 gram, then bag #1 is the low quality coins, if step 4 results 2 grams, then bag #2 is the one, if step 4 results 3 grams, then bag #3 is the one.......etc.

Ans3.
Place 3 marbles on each tray.
- If the first weighing doesn't balance, remove all the marbles from the lighter side, and place one marble on each tray from the heavier tray. The heavier side is the 1.1 ounce marble, but if they balance, then the marble from the heavier tray from the first weighing that was not weighed in the second weighing is the heavier one(1.1).
- If the marbles balance on the first weighing, remove the marbles from the trays, and place 2 of the remaining marbles not yet weighed on the trays, one on each tray. If one is heavier, it is the heavier marble(1.1), but if they balance, the remaining marble not weighed is the heavier one. 

Living

Q. Can a non-veteran man living in the Washington D.C. area be buried in Arlington National Cemetery?


Ans. No, it is not legal to bury people who are alive. 

Thing

Q. You are attending a party with some friends when one of them states that there is something in the room that everyone can touch with either of their hands, but you can only touch it with your left hand. What is it? 


Ans. Your right elbow.

Name It

Q. What belongs to you, but is mostly used by others?




Ans. Your name.

Surgeon!!

Q. A man and his son are driving home from a basketball game when they have a terrible accident. The man is taken to the emergency room for treatment and the boy is taken straight to the operating table.  The surgeon comes over to the operating table, sees the boy and says "  I can't operate on this patient, he's my son!  How can this be?




Ans. The surgeon is the boy's mother.

Can You ??

Q. Can you tell what we are: Half of Four of us are Two of us, Twice Two of us are Six of us, Twice Eight of us are Ten of us, and Twice Five of us are Eight of us? 


Ans. The letters that comprise the number words. The word two has 3 letters; therefore doubled it would be 6 letters, the word eight has 5 letters and doubled it would have 10 letters, etc.

Divide It....

Q. An Old friend of the family left $666,666 to 2 fathers and 2 sons to be split equally. After careful consideration they each happily received $222,222. Why and how was this possible? 



Ans. Although it seems there are four people, there are only 3. They encompass 3 generations...a grandfather, his son ( who is also a father), and his son. Thus there are 2 fathers and 2 sons, but only 3 people to split the money!

BookWorm

Q. On a shelf in the library, there is a 3 book set of almanacs labeled volume 1, volume 2 and volume 3. Each book is 2 1/2 inches thick, the pages being 2 inches thick and each cover is 1/4 inch thick.  A bookworm starts eating it's way from the 1st page of volume 1 and stops at the last page of volume 3.  How far did the bookworm travel? 


Ans. 3 inches.....you must visualize that when the books are on the shelf with the binders facing you that the right side of volume 1 is where page 1 is and the left side of volume 3 is the last page of volume 3. This being the case, the worm only eats through the cover of volume 1 ( 1/4 inch ), all of volume 2 ( 2 1/2 inches ), and only the cover of volume
3 ( 1/4 inch ) for a total of 3 inches.

Snail And Well

Q. A snail is at the bottom of a well and wants to get out.  He manages to crawl up the wall 3 feet each day, but at night he must rest ( after all that work during the day ) and so he slips back down 2 feet.  If the well is 30 feet deep, How long will it take him to get out?


Ans. 28 days.....the snail averages 1 foot each day, so after 27 days he has reached 27 feet. On the 28th day he crawls up 3 feet during the day, but since he is now at 30 feet and out of the well he no longer slips back 2 feet.

3d

Cute Babies

Planes

Q. Two planes take off at the same exact moment. They are flying across the Atlantic. One leaves New York and is flying to Paris at 500 miles per hour. The other leaves Paris and is flying to New York at only 450 miles per hour ( because of a strong head wind ). Which one will be closer to Paris when they meet?


 Ans. They will both be the same distance from Paris when they meet!!

Weight

Q. Which weighs more, a pound of feathers or a pound of gold? 




Ans. The answer is actually feathers. We need proof though! AND SO: From Joni- One pound of feathers is more than one pound of gold because the "pound" unit is different. The most commonly used system of weights in the US and Great Britain is the avoirdupois system, where 1 pound = 16 ounces. This is used for most solid objects, except for precious metals and gems; gold is weighed by a special system, called the troy system, where one troy pound = 12 troy ounces. Where one avoirdupois ounce is 28.35 grams, one troy ounce is about 31.10 grams. To convert from avoirdupois pounds to troy pounds, multiply the first by 1.2152 to get its equivalent in troy measurement. Therefore, one "pound" of feathers in troy weight is actually 1.2152 pounds (one avoirdupois pound), compared to one troy pound of gold. And the feathers win.

Relation

Q. Someone at a party introduces you to your mother's only sister's husband's sister in law.  He has no brothers.  What do you call this lady? 






Ans. Mother, or Mom, or whatever you call your maternal relative.

Birthday

Q. How many birth days does the average man have? 






Ans. One, he may have many Birthdays, but only one birth day!

Cigar

Q. 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? 






Ans. 6, he makes 5 originals from the 25 butts he found, and after he smokes them he has 5 butts left for another cigar.

Number

Q. What is the largest possible number you can write using only 2 numbers - just 2 numbers, no other mathematical symbols? 






Ans. 99, this is 9x9x9x9x9x9x9x9x9 or 387,420,489.

River

Q. Mom, Dad, and 2 kids have come to a river, and they find a boat. It is small and can only carry one adult or 2 kids at a time. Both kids are good rowers, but how can the whole family reach the other side of the river? 






Ans. The kids row across.  One comes back. An adult goes over, and the kid comes back.  Both kids row across again, and one comes back.  The other adult rows across and the kid comes back.  Both kids row across again

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