It’s a long time ago we had a matchstick puzzle. THis is a variant of what my old friend Biep posed me.
Make the following equation correct by moving just 1 matchstick:
Difficulty: ****/*****
New puzzles are published occasionally on the first Friday of the month. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars. You can check your solution here.
It’s a tradition on this site to publish some puzzles related to the new year. Happy New Year!
1) a^2 – b^2**/*****
Find 2 numbers a and b such that a2 – b2 = 024.
2) 1…9***/*****
Use the digits 1, 2, 3, … 8, 9 exactly to make 2024. You can use all arithmetical operations, including brackets, but don’t change the sequence of the digits.
They year 2024 is a remarkable year. Several sums can be made with the digits:
2+2=4
2*2=4
2^2=4
2+2=4+0
3) 2024 sums */*****
a) What is the next year with the same four digits?
b) How many years exist with these 4 digits?
c) What is the next year with digits a,b,c, and d such that a+c=d?
d) How many years abcd did we already have in this millenium such that a+c=d?
New puzzles are published at least once a month on Fridays. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars. You can check your solution here.
Consider
n^10 – n^5 = 2
What is the integer solution? (That is, no square roots, no complex numbers, just integer numbers)
You can find the solution here.
Last weekend we played “40 tellen” (40 count), a card game published by christian radio station Groot Nieuws Radio.
The game is simple, a player draws a card, which lists an exercise for the other players. The word on top is what the other playerts should try to guess. Below it are 4 words, which should be read one at a time. Players are free to shout their guesses any moment.
Instead of reading the 4 hint words aloud, the player my hum a suggested song, or come up with his or her own hints
Example:
The 4 hint words are apostle, bible, travels, letters.
Solution : Paul.
We played it with the 4 of us and it worked pretty well. It is one of the few instances where a company comes up with puzzle game based on inductive logic. Kudos.
*/*****
1. What are we talking about?
– Venus
– Pluto
– Mercury
– Neptune
**/*****
2. What are we talking about?
– Drill Rap
– Edgar Allen Floe
– Crunk
– Phonk
– Verzuz
A new puzzle is published at least once a month an Friday.
You can check your solutions here
You are on the Island of Zwrazr in the Logico archipelago where there are three types of people: Truth-speakers, who always speak the truth, Liars, who always lie, and Switchers, who alternate their sentences between speaking the truth and lying.
In the bar (2)***/*****
In a bar, the barkeeper shows you to a table with three people: “That table over there, with three people, has exactly one representative of each of the three groups of people on our Island.”
You introduce yourself at the table and the only woman among them says:
My friend to the left of me is a Switcher
My friend to the right of me is a Switcher
What can you say about the barkeeper?
You can check your solutions here
ChatGPT is a chat program based on a language model.
I had 2 sessions with it to test its ability to solve Bongard puzzles with language. I think its shows a severe limitation of the AI model used, though I have insufficient knowledge of AI to list
I will first list here the problems, please try to solve them yourself before turning to the solutions, where I will list the replies given by the AI bot.
Problem I*/*****
What is the difference between the sentences 1) to 6) and the sentences a) to f)?
1) What was Trumps salary as a president?
2) Why do many people like to solve puzzles?
3) How many puzzle magazines are sold yearly worldwide?
4) How many crossword puzzles has The Times published?
5) When will the next election in the Russian Federation be?
6) Who will likely be a candidate rivelling Abraham Lincoln as a president?
vs
a) Donald Trump recdeived the normalm salaray as a president
b) An oak tree can have over a thousand leaves
c) The Times published a crossword puzzle every day
d) Worldwide, puzzles are published in over 100 countries, and many magazines appear monthly.
e) It is widely regarded unlikely that the next election in the Russian Federation will be considered fair.
f) Forcing is a method used in set theory
Problem II*/*****
What is the difference between the tools 1) to 7) and the tools a) to g)?
1) Violin
2) drums
3) spanish guitar
4) irish flute
5) triangle
6) tambourine
7) organ
vs
a) Hammer
b) chisel
c) saw
d) drill
e) plane
f) pincers
g) screw driver
Problem III**/*****
what is the difference between the words in 1) to 7) and the words a) to g)?
1) float
2) make
3) produce
4) fly
5) write
6) think
7) speak
vs
a) fortress
b) idea
c) production
d) goods
e) article
f) booster
g) fire
Problem IV****/*****
What is the difference between the sentences 1) to 7) and the sentences a) – g)?
1) Jason was an argonaut
2) No duplication is OK
3) How many coins did I burn?
4) A fox obstructs my plan
5) Cats and dogs don’t munch grass
6) I saw an ox and an ass working as a pair is ridiculous
7) Who says I got no guts?
vs
a) I have no money left in my purse
b) Who says I have no courage?
c) volatile movements are normal on a stock exchange
d) Who stepped first into the elevator?
e) Gardens flower in spring
f) A sunny day raises the mood
g) “to jump” is a verb
Problem V**/*****
1) Bread can be brown
2) Bakers bake bread
3) Bookmakers bet money
4) Black is a beautiful colour
5) Bold soldiers fight on
6) Beraved of hope, the traveller sat down
7) Borrowing may cost you interest
vs
a) Shaving oneself may be a daily practice.
b) Silver is a precious metal
c) Sorry to hear that
d) Sending the message by telegraph is outdated
e) Skates can be used for matches
f) Samples are usually small
g) Singularities are abonormalities
Problem VI****/*****
1) Dogs bark loudly in our street
2) Mom bakes a delicious cake
3) Some countries ban books
4) The dad bears the financial responsibility
5) The kids become a little bit taller every day
6) Beggars beg for food
7) Christians believe the bible is true
8) The gambler bets
9) The police blocks the street
vs
a) This fish swims in the sea
b) The spy sabotaged the factory
c) The soldier salutes the flag
d) The soccer team scored another victory
e) I searched the internet in vain
f) John sharpens the pencil
g) John shaves himself
See here for the answers ChatGPT gave.
New puzzles are usually published on Friday mornings, on the first or third Friday of the month.
The two puzzles below are very easy. I am indebted to my long term friend Biep for passing this one on to me. There are some related puzzles, which you can find here and here.
Ten logicians walked into a cafe. Each knew whether they wanted tea or coffee, but no one knew each other’s preferences. When they sat at a table, the waiter asked loudly, “Will everyone be having coffee?” Then the waiter went around the table, writing down each person’s answer.
There were three possible answers: “I don’t know”, “Yes”, and “No”. All answers were truthful and spoken loudly so that all group members heard them.
I don’t know*/*****
Suppose the first nine people said, “I don’t know”, and the tenth person said, “Yes”. How many of them wanted coffee?
6the and 7th*/*****
Suppose the sixth and the seventh answers were not the same. How many people said, “I don’t know”, how many said, “No”, and how many said, “Yes”. Find the smallest number of people who for sure would have ordered coffee and the smallest number who for sure would have wanted tea?
You can check your solution here.
New puzzles are published at least once a month on Fridays. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars.
In 1967 the Russian scientist M.M. Bongard published a book containing 100 problems. Each problem consists of 12 small boxes: six boxes on the left and six on the right. Each of the six boxes on the left conforms to a certain rule. Each box on the right contradicts this rule. Your task, of course, is to figure out the rule.
A Bongard problem consists of two groups of 6 images. Each and every of the six images on the left complies wit a certain rule. Each of the 6 images on the right does NOT comply with this rule. What is the rule?
THe title of this post already says this is a math puzzle, but you’ll first have to discover which branch of math, and than you will have to think about the one symbol which doesnt seem to fit into that branch.
Whats this?****/*****
New puzzles are published at least once a month on Fridays. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars. You can check your solution here.
Of course I wish all my readers a happy 2023!
1) 2023**/*****
Find two numbers a and b such that a^2 – b^2 = 2023.
2) 2023**/*****
Show that there is just one pair.
3) Difference*/*****
How much is 20232 – 20222?
This puzzle is an adaption of https://www.youtube.com/watch?v=NOIw0VZX1lc
Christmas was somehow more busy than I expected, so I apologize for not posting these puzzles earlier. However, here are some more 2023 brainteasers:
1) https://mathequalslove.net/2023-puzzle/*/*****
Sarah Carter made a puzzle by writing out the year with digital digits and cutting it up.
2) https://paulmotwani.com/2023/01/02/blog-post-145-happy-new-year-brainteasers-%F0%9F%98%8A%E2%99%A5%F0%9F%98%8A/**/*****
Paul A. Motwani brings a nice puzzle about a product and sum, which differ 2023.
New puzzles are published at least once a month on Fridays, usually the 1rst and / or third Friday of the month. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars. You can check your solution here.
Usually the puzzles in this blog are of the type “brainteasers”, uniquely constructed puzzles. There is another type of puzzles, which I call magazine puzzles. The best know examples are crosswords and sudoku. The latter have clear rules, a fixed format, but still every puzzle is different.
The puzzles I designed for Christmas 2022 are of the latter type. For each of the following five problems, the words have been taken from the Christmas stories in the classical King James translation. This alas results in some outdated words. Your task in each of the five problems is to fit the words into the yellow boxes.
It’s a tradition on this blog to publish a special blogpost for Christmas. People tend to have days off and spend more time with their family then during ordinary weeks. There is no advanced knowledge of the English language necessary. I wish you a lot of pleasure solving these puzzles.
Churches may use these puzzles for thei sunday classes, weekly newsletter, and similar publications, as long as you mention the source and don’t sue me. Copying materials is entirely your responsibility.
1) Matthew 1 **/*****
All words are used from left to right or top-down.
appeared
begat
brethren
brought
emmanuel
example
firstborn
forth
generation
minded
people
2) Matthew 2: 1-12 **/*****
All words are used from left to right or top-down.
bethlehem
days
demanded
diligently
eat
gathered
house
jerusalem
judaea
least
opened
priests
together
troubled
3) Matthew 2: 13-end */*****
All words are used from left to right or top-down.
appeareth
called
children
comforted
destroy
egypt
enquired
herod
jeremy
lamentation
might
prophet
prophets
rachel
under
4) Luke 1 : 1-22***/*****
Words can not only be filled in top-down and from left to right, but also starting at bottom and from right to left.
appeareth
called
children
comforted
destroy
egypt
herod
jeremy
lamentation
might
prophet
prophets
rachel
under
5) Luke 1 : 22-end***/*****
Like the previous one, words can be in any direction: top-down, down to top, left to right, or right to left.
accomplished
cousin
darkness
dayspring
delivered
deserts
elisabeth
espoused
highly
hungry
joseph
leaped
ministration
neighbours
overshadow
promised
prophets
reproach
salutation
saluted
I apologize beforehand if there are any undetected errors in the puzzles. Please check them before copying them in any other medium.
You can find the solutions here.
justpuzzles 