In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half the lake?
A large jug contains 2018 nickels and 2019 dimes. Next to the jug is a large pile of dimes (treat it as an unlimited number of dimes). The following procedure is to be performed repeatedly until a single coin remains in the jug.
Two coins are chosen at random from the jug:
If both coins are dimes, one is put back and the other is discarded.
If both coins are nickels, both are discarded and a dime from the pile is added to the jug.
If one coin is a dime and the other is a nickel, the nickel is put back and the dime is discarded.
Will the last coin remaining in the jug be a nickel or a dime?
Answer: The last remaining coin will be a dime.
To see this, we observe that no matter what two coins are selected from the jug, we will always end up with one less coin in the jug after each selection as one coin is always added to the jug after two are removed. Additionally, in each selection, the number of dimes in the jug is either increased by 1 or decreased by 1, while the number of nickels either remains the same or is decreased by 2. This is summarized in the table below.
Case (coins chosen)
Net Change in the # of Dimes
Net Change in the # of Nickels
Net Change in the Total # of Coins
i. both dimes
-1
0
-1
ii. both nickels
+1
-2
-1
iii. 1 dime and 1 nickel
-1
0
-1
Since the total number of coins decreases by 1 after each selection, at some point we must have one coin remaining in the jug. However, the number of nickels is initially even (2018) and always decreases by an even amount (either 2 or 0), so it is not possible for there to ever be one nickel in the jug. Thus we conclude that the last coin in the jar must be a dime.
You are tasked with transporting 3,000 apples from Appleland to Bananaville, a distance of 1,000 miles. You have a truck that holds 1,000 apples. However, there is an apple toll on the road to Bananaville, and you must pay 1 apple per mile you drive. There is no toll when you are headed in the opposite direction, toward Appleland.
What is the largest number of apples you can transport to Bananaville?
Hint: You may leave apples on the side of the road and return to pick them up later.
SOLUTION
Obviously you cannot load up your truck with 1,000 apples and drive directly to Bananaville 1,000 miles away. All of your apples would go to the apple toll. You must devise a way to bring some apples part of the way, go back and get more, then get a full truckload to start with closer to Bananaville.
You can deliver a total of 833 apples to Bananaville. Let's see how.
First you depart Appleland with a full truckload of 1,000 apples and drive 333 miles, about a third of the way to Bananaville, and drop off the 667 apples you have left after tolls. Then you go back and repeat this process twice, which leaves you with 2,001 apples at the 333-mile mark.
The second leg of the journey is similar, but this time you will take two loads of 1,000 apples 500 miles further, which will give you 1,000 apples at the 833-mile mark with 167 miles still to go to Bananaville. (Alas, you must abandon one apple behind, for it will not fit into your truck.)
Finally, take the 1,000 apples you have left and drive the remaining 167 miles to Bananaville, arriving with 833 apples. The citizens of the noble town will surely thank you for adding a little variety to their diet.
You may have noticed a mathematical quirk to the solution. In the first step, you took three truckloads a third of the way (333 miles). But in the second step, you took two truckloads half of the overall distance (500 miles). This is the most efficient way to transport the apples because you leave yourself with the correct remaining number of apples for full truckloads, meaning products of 1,000. Because 1,000 miles doesn't cleanly divide by 3, you are forced to leave that one apple behind at the 333-mile mark of your journey.
It may have taken a bit more time than otherwise, but you have successfully brought the apple trade to Bananaville, and you paid as little as possible in apple tolls as well!
A window cleaner is cleaning the windows on the 25th floor of a skyscraper. He slips and falls. He is not wearing a safety harness and nothing slows his fall, yet he suffers no injuries. Explain.
Acting on an anonymous phone call, the police raid a house to arrest a suspected murderer. They don’t know what he looks like but they know the perp is a man named John and that he is inside the house. The police discover a carpenter, a truck driver, a mechanic and a fireman all playing poker. Without hesitation or communication of any kind, they immediately arrest the fireman. How do they know they’ve got their man?
The 60th and the 62nd Prime Ministers of the United Kingdom had the same mother and father but were not siblings. How can you account for this?
A man dressed completely in black, wearing a black mask, stands at a crossroads in a totally black-painted town. All of the streetlights in town are broken. There is no moonlight. A black-painted car without headlights drives straight towards him, but it turns in time and doesn’t hit him. How did the driver know to swerve?
Answers:
Did you assume he was cleaning the outside of the window? Ah…. He was cleaning the inside!
Did you assume all the poker players were men? The fireman is the only man present. The rest of the poker players are women.
Did you assume the 60th and 62nd prime ministers were different people? They were both Winston Churchill!
Your task is to turn over as few cards as possible to verify whether the following statement is true: Every card with a vowel on one side has an even number on the other side. You must decide in advance which cards you will examine:
Answer:
Think you’ve got the answer? Guess what…there are TWO possible (and both correct) answers. Don’t continue until you’ve given it a try.
Correct answer #1:
3 cards must be turned over:
You have to flip over “A” to make sure that it has an even number on the other side
You have to flip over “B” to make sure that it DOESN’T have a vowel on the other side
You have to flip over “7” to make sure that it DOESN’T have a vowel on the other side
The “4” need not be flipped because turning over the card can neither prove nor refute the statement “Every card with a vowel on one side has an even number on the other side”.
In many versions of this problem, it is explicitly stated that each card has a letter on one side and a number on the other. This puzzle, however, did not. If you, like many people did last week, answered that only “A” and “7” needed to flip, you likely assumed that a number had to appear on the obverse of “B.”
Correct answer #2:
This answer assumes a completely different interpretation of “side”. The puzzle doesn’t specify which sides. Instead of thinking about it as front side and back side, you can look at it as the left side and right sides of each card. In this case, the answer is zero. Looking at the left and right sides, the only card with a vowel on one side (left) is “B”. And since it also has an even number on its other side (right), you can conclude that the statement is true. No “turning over of cards” is necessary!
You have 100 pounds of potatoes, which are 99 percent water by weight. You let them dehydrate until they’re 98 percent water by weight. How much do they weigh now?
Answer: If the potatoes are 99% water, then that means there is 1 pound of non-water potato matter.
If we move to 98% water, that means the 1 pound of non-water potato matter makes up 2% of the weight.
Math : 2% of what = 1 pound? Answer : 50 (2% x 50 = 1)
A hunter walks a mile due south, turns and walks a mile due east, turns again
and walks a mile due north, only to find herself back where she started. The hunter draws a bead on a bear and shoots it dead.
What color is the bear?
Why?
Answer:
The bear you shoot will always be a polar bear, but the explanation for why this is – that the hunter must have started at the North Pole – is insufficient. While this is one possibility, the North Pole is not the only point of origin on Earth that satisfies the conditions presented in the problem. Can you think of any other point (or points) on the globe from which the hunter could begin her journey and find herself back at her original location?
Any point that is 1 + 1/(2 π) miles north of the South Pole will satisfy the conditions of this riddle's setup.
The reasoning is as follows: There is a line of latitude near the South Pole with a circumference of one mile. If one begins at a point 1+1/(2 π) miles north of the South Pole and walks one mile south, she will find herself on the mile-round line of latitude; walking one mile east will therefore bring her in a complete circle around the pole, such that when she turns and walks a mile north, she finds herself right back where she started.
1. You’re running in a race. You’re almost at the finish line when you pass the competitor in second place! What place are you in now?
A. First
B. Second
C. Third
D. Fourth
2. Before Mount Everest was discovered, what was the tallest mountain on Earth?
A. K2
B. Kanchenjunga
C. K12
D. Everest
3. There are 12 apples in a barrel. If you take away 5, how many do you have?
A. 5
B. 12
C. 7
D. 17
E. 3
4. How well do you know the U.S. presidential line of succession? If the vice president were to die, who is supposed to be president?
A. Speaker of the House
B. Attorney General
C. Secretary of State
D. President
E. Vice President
5. Imagine you’re in a pitch-black room with no electricity and you only have one match. In front of you is a candle, a gas lamp, and a fireplace. What do you light first?
A. Candle
B. Gas lamp
C. Fireplace
D. Match
6. You leave home and make one right turn, then three left turns, and then return home. Waiting for you there are two people in masks. Who are they?
A. Trick-or-treaters
B. Burglars
C. An umpire and a catcher
D. Your roommates
E. Your parents
F. Lawn decorations
7. It is high noon in the desert and there are two camels sitting still: one is facing east and the other is facing west. How do the camels see each other with no reflective surfaces and without turning their heads or bodies around?
A. The camels are walking in a circle
B. The see each other’s shadows
C. They are facing each other
D. The camels will never see each other
E. There are no camels
8. A guilty prisoner who is sentenced to the death penalty is told that he has one last chance to say something to get out of jail. If they say something true they’ll be shot and if they say something false they’ll be hanged. What do they say?
A. I’m guilty
B. I’m innocent
C. You’re going to shoot me
D. You’re going to hang me
E. I want to die
F. They don’t say anything
9. The saying does “30 days have September, April, June and November…” you know the rest. Or do you? How many months have 28 days?
A. One
B. Three
C. Four
D. Eight
E. Nine
F. Twelve
10. A man wants to marry his widow’s sister. Is that legal?
A. No, that would be considered incest, which is illegal
B. I mean it’s a jerk move, but not technically illegal…
C. This is impossible
D. They’re already married!
E. Null and void, you’re talking about the same woman.
You're placed on a medication regime in which you are to take daily one tablet of A and one of B. So, you have two little pill containers. One says "Pill A," and one says "Pill B."
You must be careful. Taking two or more B's can have unpleasant side effects or can even be fatal. In order for the B pill to be effective it must be accompanied by the A pill.
So, you open up the A bottle and you, as people do, you tap the bottle, and one A pill jumps out into your palm.
You open the B bottle, and you accidentally get two Bs falling out of the bottle. But here's the problem. They look exactly the same.
They're both blue, they're the same size, they're the same weight, with no markings on the pills. And as soon as they fell into your hand, they got mixed up, so now you have three pills, but you can't tell what the heck you have. Now, of course, you could just throw these pills away.
But the pills cost a hundred bucks apiece!
So how can you make sure that you get your daily dose of A and B without wasting any of the pills?
Answer:
And here's how you do it. You know that you have one A and two Bs. You just can't tell which are which. So let's add another A to the mix. So now, you have two As and two Bs, so you lay the four pills out in a row. But you still don't know which are which. Now, you could again go, eenie, meenie, minie, moe. And your chances of getting the right thing are improved by having done this, but not good enough, because you could die.
However, if you take each pill and cut it in half and without mixing up the halves— in other words, the first pill you cut in half, you leave those two halves near each other — and do the same thing with the second, the third, and the fourth pill.
Then you take one from each of the cut pills.
So, by definition, you know you have two As and two Bs in the mix, you'll take a half an A from one of the cut pills, and a half a B, and then another half an A, and then another half a B, and you'll have two half Bs and two half As, making one A and one B, and then the remaining pills, cut pieces, will be tomorrow's dose.
Five pieces of coal, a carrot and a scarf are lying on the lawn. Nobody put them on the lawn but there is a perfectly logical reason why they should be there. What is it?
Answer: They were used by children who made a snowman. The snow has now melted.
