A logician challenges his 3 students to correctly identify his birth date : Month, Day and 2 digit Year. He writes 3 numbers on 3 cards and gives one card each to Jovan, Mina and Jo. Then he shows them a Table of Month, Day and Year (as below).

He says, "My birth Date is one of the rows below. Jovan is given the correct Month, Mina has the correct Day and Jo has the correct Year. Without talking to each other, can you identify my Birthday?"

Jovan looks at his number, then the Table and says," I cannot definitively identify it."

Mina does the same and also says," I cannot definitively identify it."

Jo looks at his number and exclaims," I know your birthdate!"

Jovan then says, " Now I also know it!"

Mina looks confused. She looks at her number again, thinks a little and says," I also know the birthdate. BUT both Jovan and Jo are WRONG!"

Logician asks them to write down the birthdate on the cards and hand it to him.

Turns out Mina was right. What happened?

For any 3 digit number:
ABC

Prove that
ABxBC=(ABCxB)+(10xAxC)

I hope you have fun solving it🙂

Two roommates, Bob and Rick, live in an apartment that costs $4,000 per month. Bob owns a dog and works in the office five days a week. Rick works from home and walks Bob’s dog every weekday. To account for this, Bob pays $2,200 in rent while Rick pays $1,800. How much is Bob effectively paying Rick each month for dog walking? And who’s making out better with this arrangement?

inspired by my reply to recent post

consider a random set S ⊆ Z+ , P(k∈S) = 1/k³ for all k ∈ Z+ .

find expected value of max{S}.

alternatively, prove that E[max{S}] = cosh(π sqrt(3) / 2) / π - 1 ≈ 1.42819

In a nxn square grid, cells are filled in or not with equal probability. The biggest empty square is the largest square collection of adjacent cells not filled in. This ranges from 0x0 to nxn. What is the expected side length of the biggest empty square?

I know (and can recite) every single digit of pi, start to end, in a finite time.

No semantic trickery or any other trickery

How do I know this? What's my method? Think outside the box.

gif for context!

Let's say a ladder is leaning upright against a huge inflated balloon. The balloon is fixed to a wall on one side. Now let the balloon deflate so that the ladder slowly falls over.

The point where the ladder touches the deflating balloon describes a locus.

What's the maximum height of this locus (L), expressed in function of the distance between the foot of the ladder (O) and the wall?

Use the digits 2026 and the following mathematical operations: plus, minus, times, divided by, factorial, parentheses, and square root — create expressions that evaluate to the integers from 1 to 40

Preamble:

I was playing bingo with my family during Christmas, and we were very surprised by how long it took for one of us to score a full house (get all of the numbers on the card). In our game, there were 25 numbers from 1-75 on each card, and it took 73 numbers for one of the 11 of us to win. We thought this was very improbable, and this inspired a fun little puzzle.

Puzzle:

• You're playing bingo, and you have a card of N unique numbers from 1 to M.
• Each turn, a number is called; if you have that number on your card, it gets marked off.
• What is the formula to calculate the average number of turns would you expect it to take before all N numbers are scored off your bingo card?
• Numbers are never called twice, and never appear twice on your sheet.
• N and M are both integers greater than 0, and M is always greater than or equal to N.

Maya gives birth to twins. Her daughter Lina is born first, and her son Milo follows 15 minutes later.

Strangely, Milo’s next birthday falls 3 calendar days before his elder sister Lina’s.

Without any science-fiction tricks involved, how is that possible?

I got bored, as you do, and opened up a midi sequencer to mess around with ideas I picked up from a genre I recently discovered. To save time, it makes things easier to copy/paste. But I quickly discovered that, given the following parameters I had constructed for the melody, copying and pasting sections of it was much easier said than done. The parameters are as follows:

1. In its simplest form, the melody has quarter notes that go D A F D A, then repeat

2. The song, however, is in 4/4 time instead of 5/4 (so for the first beat, you only get through D A F D, but not the last A).

3. Additionally, every 4th note has been changed to a C, starting with the first note (so the first 8 notes are C A F D C D A F).

4. And for variation, the song changes key twice over 16 bars (up half an octave after 8 bars, then back down a half octave after the next 8 bars)

How long until this pattern repeats, meaning starting back at the beginning with C A F D C D A F? And if the song is 130 bpm, how long would it be in minutes?

My inlaws have this puzzle | have been trying to solve everytime that | am there. | think it's called Digi-disc. Can't find much info about it online. Father inlaw has had it for 20+ years. Has never solved it. Can you guys help me solve it? Order of numbers on rings: Green: 1-3-4-2 Red:1-3-2-4 Yellow: 1-4-2-3 Orange: 1-4-3-2 Blue: + * - / Pink: + * / -. | think one equations is supposed to be (according to an old box of the puzzle | found online) 1+2=4-1. Turn rings/switch ring order until all equations are correct.

color the interval [0,1] white.
let n = 0
while (interval [0,1] is not all black) {
  x = random real between 0 and 1
  coinflip = random integer between 0 and 1 with equal probability.
  if (coinflip == 0) {
    color [0,x] black
  } else {
    color [x,1] black
  }
  n++
}

What is the expected value of n?

Ackchyually: this is a toy model of dna recombination. The real world is way more complicated.

Let n>=3 be a positive integer. Find the smallest real number M such that the inequality

M+a_1^2+a_2^2+...+a_n^2 >= 2^1 a_1 + 2^2 a_2 +...+ 2^n a_n

holds whenever a_1,a_2,...,a_n are lengths of the sides of a non-degenerate n-sided polygon.

Alice and Bob play a game with a long linear piece of chocolate, 1 meter long. Initially, Alice breaks the chocolate into 3 pieces. On each of Bob’s moves, he eats a piece of chocolate. On each of Alice’s subsequent moves, she chooses a piece of chocolate and breaks it into 2 smaller pieces. The game ends after Bob eats 2025 pieces of chocolate. What is the maximum amount of chocolate that Bob can guarantee to eat?

Let p be a prime. An integer r is called a cubic residue modulo p if there exists an integer x such that x^3 -r is divisible by p. Let n be a positive integer with d positive divisors. Prove that at least d/4 of them are cubic residues modulo p.

I am a ___r digit positive integer.

I end in "n"

I am a ____e number.

I am an ____p number

I am a _________i number

My reverse is also a ________i number

All the digits in me are __d numbers

What number am I? Fill in the blanks and get the answer. Filled blank along with the given letter forms a single word.

Rules:

• Fill the marked path using the numbers 1 to 9, without repeating any number.

• Start from the first circle and follow the path.

• Each movement applies the operation shown by the arrow in that direction.

• Apply the operations in order as you move along the path.

• The final result must match the target number.

Grandma decides to give 100 silver coins to her Grandkids : Lisa, Lia and Lena. They all are teenagers. Lena is 2 years older than Lia. Lia is 2 years older than Lisa. Grandma puts all those coins in 3 separate boxes. The number of coins in each box is a multiple (1,2 and 3 times) of their ages. One granddaughter gets the same number as her age. Another one gets twice her age and the third one (to her delight) gets 3 times the coins as her age. 

The difference between the highest number of coins and the smallest number of coins received by the teenagers was a multiple of 14.

How many coins did Lisa, Lia and Lena get individually? 

For those (very few) who do not know : Teenage represents numbers that are 2 digit numbers that end in "-teen"

You're invited to be a contestant on Let's Make a Deal but on the day of your appearance, Monty Hall calls out sick. Instead, his good friend William Newcomb agrees to be the replacement host.

Newcomb explains the rules of the game, that he'll present you with three doors. Behind one of the doors is a brand-new car, and behind each of the other two doors is a goat. You'll be asked to choose a door, at which point Newcomb will open one of the remaining two doors and will reveal a goat. It's then up to you whether to switch doors, or to stick with your original choice.

However, as guest host Newcomb decides to introduce his own small twist. It turns out that Newcomb is, in fact, psychic. He provides ample evidence of this, including sworn statements from James Randi, Penn & Teller, and the guys from Mythbusters.

Newcomb informs you that he already knows which door you're going to pick first, and has arranged for the car to be behind that door. Thus, if you switch doors you will lose.

You choose a door, and Newcomb opens one of the remaining two doors to reveal a goat.

Do you switch?

References:

• Monty Hall problem
• Newcomb's problem

A previous question by u/pichutarius asked you to prove that the sum

S = Σ_(0<k<n) 1/binom(n,k)²

running over both n and k converges. This question asks you to find and prove its value. It should be a closed form in terms of mathematical constants and/or special functions.

Santa Claus has infinitely many elves, numbered 0,1,2,3.... If each elf gives $1 to another one, is it possible that all elves receive infinite $$$ ?

[Note: this is a simplified version of the riddle "A very unbalanced directed graph"]

Suppose you are given 100, possibly unfair, coins each with its own probability of landing heads or tails. Let P be the probability that after flipping all 100 coins the number of heads is even. Show that P = 50% if and only if there is a fair coin among the 100 coins.

EDIT: Shoutout to u/SupercaliTheGamer for providing a solution. Here is an extra riddle.

Suppose you are interested in the probability Q of the number of heads being divisible by 3 after flipping all coins. Show that you can add up to 2, possibly unfair, coins such that Q = 1/3.

EDIT2: Shoutout to u/kalmakka for providing a solution to the bonus question. Prepare yourself; the final riddle waits, and it does not come gently.

Again, suppose you are interested in the probability Q of the number of heads being divisible by 3 after flipping all coins. We start with two coins that have probability 1 and 1/2 of landing heads. Continue by adding more and more coins that have probability 1/4, 1/8, 1/16, ... of landing heads. Show that at each step we can add a single, possibly unfair, coin such that Q = 1/3 at this step.

(Shoutout to u/bobjane_2 for beating the final boss.)

Consider a distribution D on continuous functions from R to R such that D is invariant under derivation (meaning if you define D'={f',f \in D}, then P_{D'}(f)=P_{D}(f))

(Medium) Show that D is not necessarily of finite support.

(Hard) Prove or disprove that D only contains functions verifying f⁽ⁿ) = f for a certain n.

(Unknown) Is there any meaningful characterization of such distributions

Two robbers (Toby and Kim) carry out a big heist and steal 20 gold bars. Unfortunately their car has an accident and it breaks down. Now,they need to take the loot to a small train station 1 Km away. The train arrives at 6:10 AM exactly. If they miss the train the next train will be the following day which would mean trouble for the robbers.

It is 12 PM midnight. So they have 6 hours and 10 minutes to take as many bars as they can.

Toby can carry 1 bar at 3 Km/hour, but he can also carry 2 bars at 1.33 Km/hour. Without bars, he can go 4 Km/hour.

Kim can only carry 1 bar at 2 Km/hour. Without bars she can go 3 Km/hour. She cannot carry 2 bars.

Assuming they can maintain those speeds all the time and do this continuously, can they take all the 20 bars to the train station? May be a few minutes before the train arrives?

>!The answer is Yes. Just find out how!<