There are three 3L, 4L and 5L vessels, a tap with water and 3L of syrup in the smallest vessel. Is it possible to get 6 liters of a mixture of water and syrup so that there is an equal amount of water and syrup in each vessel?
Leaflet #transfusion
Leaflet #transfusion
Wikipedia
Syrup
thick, viscous liquid consisting primarily of a solution of sugar in water
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A man says: "I am a liar". Can he be a resident of the island of knights and liars?
The action in almost all problems of the leaflet #amazing_island takes place on an island whose inhabitants are knights and liars. Knights always tell the truth and liars always lie.
📜 Leaflet #amazing_island
More about liar's paradox.
The action in almost all problems of the leaflet #amazing_island takes place on an island whose inhabitants are knights and liars. Knights always tell the truth and liars always lie.
📜 Leaflet #amazing_island
More about liar's paradox.
Wikipedia
Liar paradox
statement of a liar who states that they are lying: for instance, declaring that "I am lying" or "everything I say is false"
MathProblem 💙💛 pinned «There are two identical cups: one with coffee and one with milk. A spoonful of coffee is poured from the first cup into the second cup. Then a spoonful of the resulting mixture is poured back from the second cup into the first one.
Which is bigger?»
Which is bigger?»
Each of the islanders gathered in the square said to the others: You are all liars.
How many knights are there among them?
📜 Leaflet #amazing_island
Wikipedia
How many knights are there among them?
📜 Leaflet #amazing_island
Wikipedia
Wikipedia
Knights and Knaves
logic puzzle
Two residents of the island met on the street.
One of them said: "At least one of us is a knight."
The second one answered him: "You're a liar." Which one of them is which?
One of them said: "At least one of us is a knight."
The second one answered him: "You're a liar." Which one of them is which?
Anonymous Quiz
22%
Both are knights
32%
The first is a knight, the second is a liar
20%
The first is a liar, the second is a knight
26%
Both are liars
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1) Each of the 7 residents of the island sitting at the round table said: "My neighbors are a liar and a knight."
How many knights and how many liars are sitting at the table?
2) The same question if 9 islanders were sitting at the table?
📜 Leaflet #amazing_island
How many knights and how many liars are sitting at the table?
2) The same question if 9 islanders were sitting at the table?
📜 Leaflet #amazing_island
Wikipedia
Round Table
element from the Arthurian legend
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What question do you have to ask an islander to find out if he has a pet crocodile living in his house?
💡 I remind you that there are knights and liars on the island. Knights always tell the truth and liars always lie.
🎯 Solution:
A question like this:
«If I asked, "Do you have a pet crocodile at home", would you say yes?»
Why:
1) A liar with a crocodile, always lies, would answer "no" to the question "Do you have a pet crocodile at home" and answer "yes" to my question;
2) A liar without a crocodile, similarly, "no."
3) A knight with a crocodile, always tells the truth, so "yes";
4) A knight without a crocodile, similarly, "no".
Bottom line: the resident of the island with a crocodile answers my question "yes", and without a crocodile - "no".
📜 Leaflet #amazing_island
💡 I remind you that there are knights and liars on the island. Knights always tell the truth and liars always lie.
🎯 Solution:
«If I asked, "Do you have a pet crocodile at home", would you say yes?»
Why:
1) A liar with a crocodile, always lies, would answer "no" to the question "Do you have a pet crocodile at home" and answer "yes" to my question;
2) A liar without a crocodile, similarly, "no."
3) A knight with a crocodile, always tells the truth, so "yes";
4) A knight without a crocodile, similarly, "no".
Bottom line: the resident of the island with a crocodile answers my question "yes", and without a crocodile - "no".
📜 Leaflet #amazing_island
Wikipedia
Crocodile
Crocodiles (family Crocodylidae) or true crocodiles are large, semiaquatic reptiles that live throughout the tropics in Africa, Asia, the Americas and Australia. The term "crocodile" is sometimes used more loosely to include all extant members of the order…
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A tribe of cannibals caught Robinson Crusoe. The leader said, "We would be happy to let you go, but according to our law you have to make some statement. If it turns out to be true, we'll eat you. If it turns out to be false, our lion will eat you."
What should I say to Robinson to avoid being eaten?
📜 Leaflet #amazing_island
What should I say to Robinson to avoid being eaten?
📜 Leaflet #amazing_island
Wikipedia
Robinson Crusoe
1719 novel by Daniel Defoe
Some of the islanders said that there are an even number of knights on the island, and others said that there are an odd number of liars on the island.
Can the number of islanders be odd?
Can the number of islanders be odd?
Anonymous Quiz
69%
It can
31%
It can't
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Are there three integers whose sum is 201 and whose product is 30030?
Anonymous Quiz
50%
They exist
50%
They don't exist
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9 identical candies cost $11 with change, and 13 of the same candies cost $15 with pennies. How much does one candy cost up to one cent?
📜 Leaflet #scales
📜 Leaflet #scales
Wikipedia
Penny (United States coin)
United States coin with a value of 1 cent
Three rhinos weigh the same as four hippos and one crocodile.
Which is heavier: the rhinoceros or the hippo?
Which is heavier: the rhinoceros or the hippo?
Anonymous Quiz
83%
Rhinoceros
17%
Hippo
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3 crucian carp are heavier than 4 perches.
Which is heavier: 4 crucians or 5 perches?
Which is heavier: 4 crucians or 5 perches?
Anonymous Quiz
83%
4 crucians
17%
5 perches
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A pear and a plum weigh as much as 2 apples; 4 pears weigh as much as 5 apples and 2 plums. Which is heavier: 7 apples or 5 pears?
Anonymous Quiz
44%
7 apples
56%
5 pears
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Little James was given a scale and started weighing toys. The car was balanced by a ball and 2 cubes, and the car and the cube were balanced by 2 balls.
How many cubes will balance the car?
How many cubes will balance the car?
Anonymous Quiz
23%
3
14%
4
50%
5
14%
6
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There are nuts in three boxes. The first one has 6 fewer nuts than the other two together, and the second one has 10 fewer nuts than the first and the third. How many nuts are there in the third box?
📜 Leaflet #scales
🎞 Mathematics and sex, Enjoy watching!
📜 Leaflet #scales
🎞 Mathematics and sex, Enjoy watching!
YouTube
Mathematics and sex | Clio Cresswell | TEDxSydney
Never miss a talk! SUBSCRIBE to the TEDx channel: http://bit.ly/1FAg8hB
Mathematics and sex are deeply intertwined. From using mathematics to reveal patterns in our sex lives, to using sex to prime our brain for certain types of problems, to understanding…
Mathematics and sex are deeply intertwined. From using mathematics to reveal patterns in our sex lives, to using sex to prime our brain for certain types of problems, to understanding…
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Smidge and Karlsson were each given the same pie. Karlsson started eating his pie one minute later than Smidge, and two minutes after that it turned out that Karlsson had already eaten as much as Smidge had left to eat. Prove that if Smidge and Karlsson had eaten the same pie together, they would have managed it in less than three minutes.
📜 Leaflet #scales
📜 Leaflet #scales
Wikipedia
Karlsson-on-the-Roof
fictional character in a series of children's books by Astrid Lindgren
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1) Are there two consecutive natural numbers such that the sum of the digits of each number is divisible by 4?
2) Are there two consecutive numbers with an equal sum of digits?
📜 Leaflet #yes_or_no
In all of the problems of the leaflet #yes_or_no, the answer is "Yes" or "No". If the answer is "Yes", give an example of when this might happen. If the answer is "No", you should explain why.
2) Are there two consecutive numbers with an equal sum of digits?
📜 Leaflet #yes_or_no
In all of the problems of the leaflet #yes_or_no, the answer is "Yes" or "No". If the answer is "Yes", give an example of when this might happen. If the answer is "No", you should explain why.
Wikipedia
Divisor
In mathematics, a divisor of an integer
n
,
{\displaystyle n,}
also called a factor of
n
,
{\displaystyle n,}
is an integer
m
…
n
,
{\displaystyle n,}
also called a factor of
n
,
{\displaystyle n,}
is an integer
m
…
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Robert says, "The day before yesterday I was only 10 years old, but next year I'll be 13."
Can that be?
Can that be?
Anonymous Quiz
75%
Yes
25%
No
The monkey and the coconuts
Five men and a monkey were shipwrecked on an island. They spent the first day gathering coconuts. During the night, one man woke up and decided to take his share of the coconuts. He divided them into five piles. One coconut was left over so he gave it to the monkey, then hid his share, put the rest back together, and went back to sleep.
Soon a second man woke up and did the same thing. After dividing the coconuts into five piles, one coconut was left over which he gave to the monkey. He then hid his share, put the rest back together, and went back to bed. The third, fourth, and fifth man followed exactly the same procedure. The next morning, after they all woke up, they divided the remaining coconuts into five equal shares. This time no coconuts were left over.
How many coconuts were there in the original pile?
Five men and a monkey were shipwrecked on an island. They spent the first day gathering coconuts. During the night, one man woke up and decided to take his share of the coconuts. He divided them into five piles. One coconut was left over so he gave it to the monkey, then hid his share, put the rest back together, and went back to sleep.
Soon a second man woke up and did the same thing. After dividing the coconuts into five piles, one coconut was left over which he gave to the monkey. He then hid his share, put the rest back together, and went back to bed. The third, fourth, and fifth man followed exactly the same procedure. The next morning, after they all woke up, they divided the remaining coconuts into five equal shares. This time no coconuts were left over.
How many coconuts were there in the original pile?
Wikipedia
The monkey and the coconuts
The monkey and the coconuts is a mathematical puzzle in the field of Diophantine analysis that originated in a short story involving five sailors and a monkey on a desert island who divide up a pile of coconuts; the problem is to find the number of coconuts…
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