You have 10 stacks of 10 coins. You know how much the coins should weigh. You know all the coins in one stack of ten are exactly a hundredth of an ounce off, making the entire stack of ten coins a tenth of an ounce off. You also know that all the other coins weigh the correct amount. You are allowed to use an extremely accurate digital weighing machine only once.
How do you determine which stack of 10 coins is faulty?
Answer:
One coin from the first stack is placed on the scale along with two coins from the second stack and three coins from the third stack etc…
If the weight is off by one hundredth of an ounce then it is the first stack that is faulty.
If the weight is off by two hundredths of an once then it is the second stack that is faulty.
If the weight is off by three hundredths of an once then it is the third stack that is faulty.
A magical elf has a sack of infinite gifts. Every day starting December 1st, the elf places double the gifts from the previous day under the tree. On December 25th, the tree is full. On what day was the tree exactly half-full?
Answer: December 24th. Explanation: Since the number of gifts doubles daily, the tree would have been half-full the day before it was full.
Susan and Lisa decided to play tennis against each other. They bet $1 on each game they played. Susan won three bets and Lisa won $5. How many games did they play?
Answer: Eleven. Because Lisa lost three games to Susan, she had lost $3 ($1 per game). So, she had to win back that $3 with three more games, then win another five games to win $5.
Three puzzles to keep your brain flexible for today:
A California farmer owns a beautiful pear tree. He supplies the fruit to a nearby grocery store. The store owner calls the farmer to see how much fruit is available for him to buy. The farmer knows the main trunk has 24 branches. Each branch has exactly 12 boughs and each bough has exactly 6 twigs. Since each twig bears one piece of fruit, how many plums will the farmer be able to deliver?
A woman is sitting in her hotel room and hears a knock at the door. She opens the door to see a man whom she’s never met before. He says, “I’m sorry, I have made a mistake, I thought this was my room.” He then goes down the corridor and into the elevator. The woman goes back into her room and calls security. What made the woman so suspicious of the man?
If you have me, you want to share me. If you share me, you haven’t got me. What am I?
Answers:
None—a pear tree doesn’t grow plums
If he really thought it was his hotel room, he would have tried to open the door—not knock on it first.
Test your Independence Day knowledge with these 10 true or false questions!
On July 4th the Continental Congress voted in favor of declaring Independence from Great Britain.
It was not until 1941 that July 4th became a paid federal holiday for federal employees.
The Declaration of Independence was signed on July 4th, 1776.
Pennsylvania became the first state to make the 4th of July an official state holiday in 1781.
A United States President actually dies after eating spoiled fruit at a July 4th celebration.
Four US Presidents died ON July 4th.
Starting in 1818, new stars and stripes were added to the American flag each Juy 4th to mark the creation of new states
One World Trade Center in New York is 1,776 feet tall to mark the year the US declared its independence from Great Britain
As of 2016, July 4 was the number two holiday (after the Superbowl) for beer sales in the US, according to the National Beer Wholesalers Association
Nathan’s Famous Hot Dog Eating Contest is held annually on July 4th. In 2018, champion Joey Chestnut ate 74 hot dogs with buns in just 10 minutes.
Answers:
FALSE - On July 2, 1776, the Continental Congress voted in favor of declaring independence from Great Britain. The Declaration of Independence was officially adopted two days later, marked by the ringing of the Liberty Bell at Independence Hall in Philadelphia. At the time, John Adams believed that July 2, not July 4, would be the date remembered by history.
TRUE – it became a federal holiday in 1870, but a PAID holiday for federal employees in 1941
FALSE – July 4th is the date that it was formally adopted by the Continental Congress, but it wasn’t signed by most signatories until August.
FALSE - Massachussetts became the first state to make the 4th of July an official state holiday in 1781.
TRUE – President Zachary Taylor died from this in 1850.
FALSE – But THREE US Presidents HAVE died on July 4th – Thomas A Jefferson, John Adams, and James Monroe
You have two ropes. Each burns completely in exactly one hour. However, they are different lengths and thus burn at different rates. Also, along each rope the width & material changes, so they burn at different rates at different places. The only thing you know is that they each burn completely in one hour exactly.
You have a lighter. How do you measure exactly 45 minutes?
Answer: Because they both burn inconsistently, you can’t just light one end of a rope and wait until it’s 75 percent of the way through. But, this is what you can do: Light the first rope at both ends, and light the other rope at one end, all at the same time. The first rope will take 30 minutes to burn (even if one side burns faster than the other, it still takes 30 minutes). The moment the first rope goes out, light the other end of the second rope. Because the time elapsed of the second rope burning was 30 minutes, the remaining rope will also take 30 minutes; lighting it from both ends will cut that in half to 15 minutes, giving you 45 minutes all together.
The two leading mathematicians in the kingdom, Alice and Bob, have run afoul of their tyrannical king. Rather than behead them outright, the king decides to prolong their misery by locking them in separate dungeons, so that any communication between them is impossible.
Each morning, a guard is to enter the corresponding dungeon and toss a coin so that the prisoner in that dungeon can see the outcome. Then the prisoner will be asked to guess the outcome of the coin toss in the other dungeon (i.e., Alice has to guess the outcome of the toss witnessed by Bob, and Bob has to guess the outcome of the toss witnessed by Alice). If at least one of the two prisoners guesses correctly, they will live to see another day. Otherwise they will be put to death forthwith.
It would seem that the mathematicians are doomed. But as they are being led away in chains Alice and Bob manage to confer for a brief moment and they agree on a strategy that will delay their execution indefinitely. What is the strategy?....
Answer: If Alice gets heads, she will guess that Bob also got heads, and if she gets tails she will guess that Bob also got tails. Meanwhile, if Bob gets heads he will guess that Alice got tails, and if he gets tails he will guess that Alice got heads. Then exactly one of them will always be right.
The simplest way that I can see of explaining this solution is that the outcomes of the two coin tosses must be either the same or different, so one of the mathematicians should always guess that they were the same, and the other that they were different. It’s irrelevant whether the coins are fair or not.
The solution is simple, but there's still a slightly magical flavor to it in my mind. What I find so remarkable is that, for the strategy to work, both Alice and Bob need to see the outcome of their own coin toss, even though it’s totally uncorrelated with the outcome of the other’s toss!
An old man living alone in South Armagh, whose only son was in Long Kesh Prison, didn't have anyone to dig his garden for his potatoes. So he wrote to his son about his predicament.
The son sent the reply, "For HEAVENS SAKE, don't dig the garden up, that's where I buried the guns!!!!!"
At 3 AM the next morning, a dozen British soldiers turned up and dug the garden for 3 hours, but didn't find any guns.
Confused, the man wrote to his son telling him what had happened, asking him what he should do now?
A Texan walks into a pub in Galway, Ireland and raises his voice to the crowd of drinkers. He shouts, 'I hear you Irish are a bunch of drinkin' fools. I'll give $500 American dollars to anybody in here who can drink 10 pints of Guinness back to back.'
The room is quiet and no one takes of the Texan's offer.
Paddy Murphy gets up and leaves the bar. Thirty minutes later, he shows back up and taps the Texan on the shoulder. Is your bet still good?' asks Paddy.
The Texan answers, 'Yes', and he orders the barman to line up 10 pints of Guinness.
Immediately, Paddy downs all 10 pints of beer, drinking them all back to back. The other pub patrons cheer and the Texan sits down in amazement. The Texan gives the Irishman the $500 and asks, 'If ya don't mind me askin', where did you go for that 30 minutes you were gone?'
Paddy Murphy replies, 'Oh................... I had to go to the pub down the street to see if I could do it first.'
