#math puzzles

[dehex18]

Something I really like about doing math/logic puzzles is how a given puzzle can initially feel so opaque and overwhelming, but then you just start to work on one part of it. It may be slow at first, but you eventually hit a tipping point. Then, the puzzle almost seems to solve itself and it's just a matter of how quickly your hands can add the remaining parts of that solution.

[cecilias-cool-stuff]

Here's a Pete Winkler classic:

You are playing a game against your adversary Bob. There are four indistinguishable coins on a tray, say in positions North, West, South, and East, each starting as either heads or tails according to Bob's liking. Bob can always see the tray, and you never can. A single turn consists of the following:

1. You ask Bob to flip any number of coins by referring to their position.

2. Bob rotates the tray to his liking (you do not get to know how the tray is being rotated, and he must rotate it by a multiple of 90°).

You win the game if you make all of the coins heads after finitely many turns, and Bob wins if you give up. There is a strategy that guarantees your victory. What is it?

Example and bonus question below the cut.

Example:

Maybe Bob chooses the following initial position:

H

T T

H.

You ask Bob to flip North and East, so the position becomes

T

T H

H.

Then Bob rotates the tray 90° to the right and the position becomes

T

H T

H.

It is now your turn again, and the game continues. At no point could you see anything on the tray, and you don't know how much Bob rotated it - for all you know, he could have not rotated it at all!

Bonus question: If there are only three coins, Bob has a winning strategy. What is it?

[pilferedinstagram]

[thescienceofdeductionandmore]

Anna's Special Birthday

Anna thought to herself:

“If you add up the digits in my birthday (stated in month/date format) and then add the digits in the result until you have a one-digit number, you get 3. If you do that with John Lennon’s birthday, you get 1. If you do it with Paul McCartney’s birthday, you get 5.

"Oh, wow! My birthday is the average of John and Paul’s birthdays. That’s amazing. I have like the best birthday ever. Yay, for my special birthday.”

Anna’s birthday is in the first half of December. What is it?

[tramon81]

Ok any matematicians and probabilistic studies experts you might find this of interest. So let's say we have an exam with option A and B. Those exams have 2 questions each, which entail only a matter each and said matter can't be repeated between questions in the same option or between them. Now let's say that there are x matters which are part of the exam's object of study and you study y. What formula would define the probability of:

1. Getting 1 out of 2 answers right on the exam given that you can choose between A and B.

2. Getting 2 out of 2 given the same circumstances.

I don't know the answer to this question so this isn't a puzzle but a question.

[mathpiirates]

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Math is all about becoming a creative thinker not a calculator.

[mymathematics]

Ladder And Box Puzzle

Ladder And Box PuzzleLadder And Box PuzzleSpecial thanks this month to: Michael Anvari, Kyle. Thanks to all supporters on Patreon! A ladder leans against a wall, just touching the corner of a cubical box. If the ladder has a length of 4, and the box has a side of 1, what is the distance between the top of the box and the top of the ladder?

[posingasme]

I know some of you are feeling bored, unable to partake of your usual activities. It’s also important to keep your mind sharp to stave off anxiety. If you have time, this needs solving: The Riemann Hypothesis

It’s been long enough. Let’s get this solved.

https://en.m.wikipedia.org/wiki/Riemann_hypothesis

Riemann hypothesis - Wikipedia

Riemann hypothesis - Wikipedia

Tag your smartest follower/mutual for their solution or reaction!

What do you think?! @rodiniaorzetalthepenquin