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Huey has 3 donuts, Dewey has 5 donuts. Louie comes along and the three of them split the donuts equally. In exchange, Louie offers 8 candies to Huey and Dewey. What is the fair way to split the candies?
Huey must take 1 chocolate, and Dewey must take 7. This is because each of them ate 8/3 donuts, and therefore Huey gave away 1/3 of a donut, whereas Dewey gave away 7/3 of a donut.
None of these statements is correct.
At most 1 of these statements is correct.
At most 2 of these statements are correct.
…
At most 98 of these statements are correct.
At most 99 of these statements are correct.
How many of these statements are correct?
If the number of true statements is X, then statements 1, 2, … , X are wrong, and the rest are correct. Therefore X = 100 – X and X = 50. Thus, there are 50 correct statements.
You must find a 3-digit number. You know that:
What is the number?
The first and second clues imply that the 6 is not a part of the number. The third clue then implies that 2 and 9 are parts of the number. Now the first clue implies that 2 is the last digit of the number, and the third clue implies that 9 is the first digit of the number. Finally, the second clue implies that 4 is the second digit of the number. Therefore, the number is 942.
Harry Ape robbed a bank yesterday and has been hiding in the bitterly cold forest. Max Mouse found Harry’s clothes near a hole in the pond ice. Why does Slylock Fox believe that Harry is nearby?
Slylock thinks Harry fell through the ice, and after climbing out of the water, took off his wet clothes due to the frigid temperatures. The sleuth suspects the ape is nearby because the wet clothes are still unfrozen.
You need to cross a river, from the north shore to the south shore, via a series of 13 bridges and six islands, which you can see in the diagram below. However, as you approach the water, a hurricane passes and destroys some (possibly none/all) of the bridges. If the probability that each bridge gets destroyed is 50%, independently of the others, what is the chance that you will be able to cross the river after all?
Imagine there is a captain on a ship, who wants to sail through the river from West to East. You can see that he will be able to do this if and only if you are not able to cross the river. However, if you rotate the diagram by 90 degrees, you can also see that the probability that you cross North-South is equal to the probability that he sails West-East, and therefore both probabilities are equal to 50%.
Consider an arbitrary acute triangle ABC. Let E be the intersection of the bisector at vertex C and the bisection of the side AB. Let F and G be the projections of E on AC and BC respectively.
Since E belongs to the bisection of AB, we must have AE = BE. Also, since E belongs to the bisector of C, we must have EF = EG. However, this would imply that triangles AEF and BGF are identical, and then AF = BF. We also have that CF = CG, which implies that AC = BC. The arbitrarily chosen triangle ABC is isosceles!
Can you find where the logic fails?
The bisector of C and the bisection of AB always intersect outside the triangle, on the circumcircle. One of the points F and G always lies on the segment AC or BC, and the other one does not.
If Erica lives in New York and Tina lives in Buenos Aires, where does Mark live?
New York is the largest city in the United States of Am-Erica. Buenos Aires is the largest city of Argen-Tina. Therefore Mark lives in Den-Mark’s largest city – Copenhagen.
Can you find what the following abbreviations stand for?
24 H in a D = 24 Hours in a Day
26 L of the A = ???
7 D of the W = ???
7 W of the W = ???
12 S of the Z = ???
66 B of the B = ???
52 C in a P (W J) = ???
13 S in the U S F = ???
18 H on a G C = ???
39 B of the O T = ???
5 T on a F = ???
90 D in a R A = ???
3 B M (S H T R) = ???
32 is the T in D F at which W F = ???
15 P in a R T = ???
3 W on a T = ???
100 C in a R = ???
11 P in a F (S) T = ???
12 M in a Y = ???
13 is U F S = ???
8 T on a O = ???
29 D in F in a L Y = ???
27 B in the N T = ???
365 D in a Y = ???
13 L in a B D = ???
52 W in a Y = ???
9 L of a C = ???
60 M in a H = ???
23 P of C in the H B = ???
64 S on a C B = ???
9 P in S A = ???
6 B to an O in C = ???
1000 Y in a M = ???
15 M on a D M C = ???
24 H in a D = 24 Hours in a Day
26 L of the A = 26 Letters of the Alphabet
7 D of the W = 7 Days of the Week
7 W of the W = 7 Wonders of the World
12 S of the Z = 12 Signs of the Zodiac
66 B of the B = 66 Books of the Bible
52 C in a P (W J) = 52 Cards in a Pack (Without Jokers)
13 S in the U S F = 13 Stripes in the United States Flag
18 H on a G C = 18 Holes on a Golf Course
39 B of the O T = 39 Books of the Old Testament
5 T on a F = 5 Toes on a Foot
90 D in a R A = 90 Degrees in a Right Angle
3 B M (S H T R) = 3 Blind Mice (See How They Run)
32 is the T in D F at which W F = 32 Degrees is the Temperature in Fahrenheit at which Water Freezes
15 P in a R T = 15 Players in a Rugby Team
3 W on a T = 3 Wheels on a Tricycle
100 C in a R = 100 Cents in a Rand
11 P in a F (S) T = 11 Players in a Football (Soccer) Team
12 M in a Y = 12 Months in a Year
13 is U F S = 13 is Unlucky For Some
8 T on an O = 8 Tentacles on an Octopus
29 D in F in a L Y = 29 Days in February in a Leap Year
27 B in the N T = 27 Books in the New Testament
365 D in a Y = 365 Days in a Year
13 L in a B D = 13 Loaves in a Baker’s Dozen
52 W in a Y = 52 Weeks in a Year
9 L of a C = 9 Lives of a Cat
60 M in an H = 60 Minutes in an Hour
23 P of C in the H B = 23 Pairs of Chromosomes in the Human Body
64 S on a C B = 64 Squares on a Chess Board
9 P in S A = 9 Provinces in South Africa
6 B to an O in C = 6 Balls to an Over in Cricket
1000 Y in a M = 1000 Years in a Millennium
15 M on a D M C = 15 Men on a Dead Man’s Chest
Suppose you have 10 people with different heights in one row. Show that you can always remove 6 of them, so that the remaining 4 are arranged with respect to their heights (either increasing or decreasing).
Mark the first person with number 1. Look for the next person after him, who is taller, and also mark him with number 1. Then look for the first person after the second one, who is taller, and also mark him with number 1. If you find a fourth one, then you already got the four people you are looking for.
If not, mark the first unmarked person with number 2. Look for the next unmarked person after him, who is taller, and also mark him with number 2. Continue with the procedure, until you either find 4 people in the line, whose heights are increasing, or have people who are marked with numbers 1, 2, 3 and 4.
Now pick a person, who is marked with number 4. Then look for the closest person on the left, who is marked with number 3, pick him up. He will be taller, because otherwise the first person would have been labeled 3 as well. Similarly, look for the closest person, marked with 2, on the left of the last one, pick him up. Repeat this once again and you will find 4 people in the line, whose heights are decreasing.
Tools were stolen from a construction site. Max Mouse found footprints and a tire track, leading him to believe there were two thieves – one walking and the other riding a bike. Even though Slylock Fox believes both tracks are related to the robbery, he suspects there was only one thief. Why?
The tire track cannot be from a bike. The tracks were left by one thief pushing a wheelbarrow, full of stolen tools.
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