Puzzle Sum 7
What birds do these sums spell?
SOLUTION
WRENCH + ARM – CHARM = WREN
MAGNET – NET + PIE = MAGPIE
Knocked Off Piece
The following position occurs in a real game, right after one of the pieces gets knocked off the board. What was the piece?
SOLUTION
It was a black knight. First, notice that the black pawns have moved 14 times diagonally and thus they have taken 14 pieces. Therefore the knocked off piece is black. Since it is impossible for both kings to be checked at the same time, the missing piece was positioned on a2. It couldn’t be a queen or a rook, because the white king would be checked both by it and the pawn on b3, which is impossible. Therefore the missing piece is either the black white-squared bishop or the black knight. However, the pawns on b7 and d7 haven’t been moved the entire game and then the black white-squared bishop hasn’t either. Thus we conclude that the knocked off piece is a black knight.
Tetris Puzzle
As a birthday present last year, I received some fridge magnets. They didn’t come as a puzzle, so I don’t know if they have a solution, but I made a puzzle out of them anyway. The magnets are tetrominoes. There are 7 of each shape. Is it possible to arrange them into a 7×28 rectangle so that they are all used and all inside the rectangle? The closest I have managed is this:
SOLUTION
No, it is impossible. Imagine you are placing the tetrominoes on a 7×28 chess board. All of them, except for the T-shaped ones cover exactly 2 black and 2 white cells. Each of the T-shaped tetrominos covers either 2 more black cells than white cells or 2 more white cells than black cells. Since there are 7 of them, combined they will cover either more black cells than white cells or more white cells than black cells. Therefore all pieces on the picture can not cover perfectly a rectangle, which contains an equal number of black and white cells.
Source:
Out of Place
Which of the numbers below is out of place and why?
1011, 2223, 3940, 5646, 8910
SOLUTION
Every number except 5646 can be split into a sequence of consecutive numbers: 1011~10-11, 2223~22-23, 3940~39-40, 8910~8-9-10.
Math Jokes
Who says science jokes are not funny? Below you can see some of the best Math jokes we know, along with short explanations to the more obscure of them.
Do you know any funny Math jokes yourself? Let us know in the comment section below.
“Why did you divide sin by tan?”
“Just cos.”
Explanation
When you divide sinus (sin) by tangent (tan), you get
Let epsilon be smaller than zero…
Explanation
Rather silly math joke, based on the fact that the variable epsilon is always chosen to be a small positive number.
“What does the ‘B’ in Benoit B Mandelbrot stand for?”
“Benoit B Mandelbrot.”
Explanation
Benoit B Mandelbrot is a famous Mathematician, who was interested in fractals. Fractals are natural sets which exhibit repeating patterns. If you keep replacing the middle “B” in the name with “Benoit B Mandelbrot”, you will get a fractal.
A biologist, an engineer, and a mathematician were observing an empty building. They noted two people entering the building and sometime later observed three coming out.
The biologist remarked, “Oh they must have reproduced.”
The engineer said, “Our initial count must have been incorrect.”
The mathematician stated, “Now if one more person goes into the building it will be completely empty.”
At a party for functions, eˣ is at the bar, looking despondent. The barman says:
“Why don’t you go and integrate?”
eˣ replies:
“It would not make any difference.”
Explanation
If you integrate the function eˣ, you get again eˣ, i.e. it doesn’t change.
“Why can’t atheists solve non-linear equations?”
“Because they don’t believe in higher powers.”
Explanation
Non-linear equation contain high powers of the variables.
“Why did the chicken cross the Mobius strip?”
“To get to the same side.”
Explanation
The Mobius strip is a non-orientable surface which has only side. You can make a Mobius strip by taking a strip of paper, twisting it 180 degrees and gluing its opposite ends.
There are 10 types of people in this world. Those who understand binary and those who don’t.
Explanation
The number 2 is written as “10” in binary system.
Three logicians walk into a bar. The bartender says, “Do you all want something to drink?”
The first logician says, “I don’t know.”
The second logician says, “I don’t know.”
The third logician says, “Yes.”
Explanation
Even though all three of them want to drink, none of the logicians can reply “yes” unless he is sure that his friends also want to drink. Since the first two replied with “I don’t know”, the third one already knows that all of them are thirsty and says “Yes”.
There are two types of people in the world. Those who can extrapolate from incomplete data.
Explanation
“To extrapolate” means to deduce information from incomplete data.
A logician’s wife is having a baby. The doctor immediately hands the newborn to the dad. His wife asks impatiently, “So, is it a boy or a girl?” The logician replies, “Yes.”
Explanation
Since the baby is either a boy or a girl, the answer to the question (regarded as a logic inquiry) is in both cases “Yes”.
An infinite amount of mathematicians walk into a bar.
“I’ll have a pint,” says the first one.
“Half a pint for me please,” says the second one.
“Quarter of a pint please barkeep,” says the third one.
After 5 minutes of ordering, the barman interrupts the mathematicians:
“Look, here you are 2 pints of beer, you figure it out yourselves.”
Explanation
The amounts of beer the mathematicians order forms an infinite arithmetic progression – 1, 0.5, 0.25, etc., which has a total sum 2.
Three foreigners – a businessman, a physicist, and a mathematician, are talking about the country they are all visiting for the first time.
Suddenly, the businessman points out the window in surprise. “Look at that! The sheep in Scotland are black,” he says.
Amused at how readily his new friend jumps to conclusions, the physicist corrects him: “No, all we can be certain of is that some of the sheep in Scotland are black.”
The mathematician looks out the window himself, and corrects both of them: “We know there exists a sheep in Scotland which is black at least on one side.”
Two random variables were talking in a bar. They thought they were being discrete but I heard their chatter continuously.
Explanation
Wordplay with the two types of random variables in probability theory – discrete and continuous.
There was a statistician who drowned crossing a river… The river was 3 feet deep on average.
“Why did the chicken cross the road?”
“The answer to the question is trivial and is left to the reader as an exercise.”
Explanation
Many times a professor who can’t remember or doesn’t want to prove some more technical result in class, leaves it as an “exercise” for the students.
A physicist and a mathematician are sitting in a faculty lounge. Suddenly, the coffee machine catches on fire. The physicist grabs a bucket and leap towards the sink, filled the bucket with water and puts out the fire.
Explanation
One common approach for solving mathematical problems is reducing them to other, already solved problems, then making a reference to them.
When a statistician passes the airport security check, they discover a bomb in his bag. He explains. “Statistics shows that the probability of a bomb being on an airplane is 1/1000. However, the chance that there are two bombs at one plane is 1/1000000. So, I am much safer…”
Explanation
Even though the statement is correct, the statistician is not taking in account conditional probability. Obviously, his chances for safe flight are not changing by bringing a bomb.
An engineer, a physicist, and a mathematician are staying in a hotel.
The engineer wakes up in the middle of the night and smells smoke. He goes out into the hallway and sees fire, then goes back to the room, fills a trash can with water, and douses it.
Later, the physicist wakes up and smells smoke. He opens his door and sees a fire in the hallway. He walks down the hall to a fire hose and after calculating the flame velocity, distance, water pressure, trajectory, etc. extinguishes the fire with the minimum amount of water and energy needed.
Later, the mathematician wakes up and smells smoke. He goes to the hallway, sees the fire and then the fire hose. He thinks for a moment and then exclaims, “Ah, a solution exists!”, then goes back to bed.
Explanation
In many mathematical
A chemist, a physicist, and a mathematician are stranded on an island when a can of food rolls ashore. The chemist and the physicist
Explanation
Many mathematical proofs are based on various assumptions, which can be sometimes way too strong.
A physicist and an engineer are in a hot-air balloon. Soon, they find themselves lost in a canyon somewhere. They yell out for help: “Hellooooo! Where are we?” Fifteen minutes later, they hear an echoing voice: “Hellooooo! You are in a hot-air balloon!”
The physicist says, “That must have been a mathematician.”
The engineer asks, “Why do you say that?”
The physicist replies: “The answer was absolutely correct, and it was utterly useless.”
Explanation
Many people consider mathematics to be very exact, but useless for real life.
“Why don’t you see quaternions ride the bus?”
“Because they do not commute!”
Explanation
Quaternions are a number system, extension of the complex numbers. Quaternions do not possess the commutative property, i.e.
Two Games at Once
The Devil offers you a deal – you have to play two games of chess simultaneously against the two best GrandMasters in the world, one with black pieces and one with white pieces. If you win at least 1 point from the two games, you will get whatever your heart desires, if you don’t – you will go straight to Hell. Would you accept the challenge?
SOLUTION
Accept the challenge. You can easily get 1 point by just repeating the moves of your opponents. For example, if the white GrandMaster plays e4, then you play e4 against the black GrandMaster. If the back GrandMaster plays e5, then you play e5 against the white GrandMaster and so on.
Penrose Railway Maze 1
Get from START to FINISH, moving only over smooth lines, without reversing and making sharp turns.
SOLUTION
The solution is shown below.
Magic Liquid
You buy a bottle with a letter from the merchant, the merchant tells you that when you drink the liquid in the bottle it grants you eternal life, he supposedly deciphered this from the letter.
After you get home you decide to study the letter if it really says what the merchant told you, can you figure out if the bottle really grants eternal life?
You come to a fork in the road.
To the left is an empty well made from stone.
On the right is a pirate’s buried treasure.
Ahead you only see a tall straight tree.
The night is dark with only a dying moon in the sky.
Source: Puzzling StackExchange
SOLUTION
The objects described in the last paragraph have the following shapes:
fork in the road = T
empty well = O
buried treasure = X
straight tree = I
dying moon = C
The 5 letters form the word “TOXIC”, which suggests you shouldn’t drink from the bottle.
Bottle, Coin and Cork
You put a little coin in an empty wine bottle and then insert the cork in its opening. How can you remove the coin without taking out the cork or breaking the bottle?
SOLUTION
Push the cork inside and then take out the coin.
Puzzle Sum 6
What state does this sum spell?
SOLUTION
KENNEL + INK – LINK + STONE – NEST – ONE + TUCK + YEAR – EAR = KENTUCKY