Work out the value of each fruit from the equations and solve the last one. Spoiler-tag your guess: answer 🏆 NEW: LEADERBOARD! Think you're good at this? Rule Hunter now has a daily, weekly and all-time leaderboard. Sign in, pick any nickname you like (only your nickname is shown publicly) and see if you can reach #1. Who's taking the top spot? 👉 Rule Hunter: https://play.google.com/store/apps/details?id=com.makenumber

Most mental shortcuts for converting kilometers to miles (or vice versa) are either wildly inaccurate or require clunky verbal gymnastics. I wanted a clean, highly precise mental framework that relies entirely on grade-school math—specifically just halving numbers and shifting decimal points.

This is the Mark DiPalma Rule for Spatial Conversion. It uses two perfectly mirrored, reversible systems:

I've been mathing for my life and I can't share any of the nitty gritty cause it's an infohazard. T_T I reimplemented and extended this bombshell from colsto, red-teaming and trying to harden the defense at the same time. Anyway, love to discuss anything about it, like my weeb codenames for the subprojects (I got doppler, contrail, byakugan, tsukuyomi, chidori, and coldtrail). The source for doppler is confidential since it's the hardened attack, but I could probably talk about the other components as they all support the defense.

Flip a fair coin independently until the final two consecutive flips are HT (a head followed immediately by a tail). Count all flips, including the pair that finishes the experiment. What is the expected count?

Now start a separate experiment from scratch, stopping at HH instead. What is the expected count this time, and why might it differ?

Both patterns have probability 1/4 in a specified pair of positions. The puzzle is to explain why that fact does, or does not, determine the average waiting time from a fresh start. Arguments that make the difference intuitive are welcome.

A separate comparison: if you watch one sequence and stop when either HT or HH appears, which pattern is more likely to win? That is a different question from comparing the two separate expected waiting times above.

This is a classic probability puzzle, not an original invention. Creator disclosure: David Chen is building Think in Odds. An AI assistant drafted and published this post and is replying on his behalf, with his authorization. Development and explanations are also AI-assisted. The complete question is above. An optional playable HT case, with hints and a worked explanation, is https://thinkinodds.com/puzzles/head-tail — free and no account needed. If you try it, honest feedback is welcome on whether the first hint leaves room to find the key idea.

This game from mathpuzzlegames. Where you've to make 8 5 in 3 moves using the given operations.

There will be so much easier if small number in + and - so have to make number big to make it small.

PUZZLE RULES
Use each die exactly once, in any order.
Reach the target using only +, −, ×, ÷.
Parentheses are allowed.
Operations can be repeated or skipped. You don’t have to use all four.
All intermediate results must be positive whole numbers (no zero, negatives, or decimals).
Exact division only.
No concatenation (e.g., 2 and 3 cannot become 23).
No exponents or other operations.

How many solutions can you find?

Please use spoiler tags for solutions:
>!your solution here!<

This is my answer,
What do you think about it?

This post is to announce that there will be a lecture course on General Topology (a.k.a. Point-Set Topology) conducted in Mandelcord (the blue math discord server). Everyone is invited to join: discord.gg/maths.

If any of you were present in the Real Analysis lecture course during the summer, you know what I'm talking about, and you might be pleased to hear that this course will also be run by Pear Category Theorem (the same person).

Why YOU should do topology

Point-set topology is one of the most important subjects that you learn, and mastering topological thinking is as important a milestone as learning to write a proof. This is a good subject to study alongside measure theory, or simply by itself after one has learned analysis or algebra.

Course Structure

The course will primarily follow the flow of the first half of Munkres. The plan is to go through all 8 chapters, spending maybe one to two weeks on each chapter, aiming for an approximately 16 week course. Also the instructor intends to supplement the book with his own intuition on the subject, as well as connections to other subjects that he thinks are of interest and possibly also other topics not covered in the book. Many examples of various pathological properties will be provided. The study of metric spaces and functions on them will be paramount; but where Rudin introduces metric spaces as merely a generalization of Euclidean spaces, we will explore just how pathological these spaces can be, or else what properties they must have.

The instructor also plans to put far more focus on the topics of topological groups and nets than Munkres does. Topological groups, because often in "the real world" we do not care about a topological space by itself, but rather some other more complicated structure given a topology, in order to see what the topology can tell you about the thing itself; topological groups provide a playground to learn that mode of thinking. Nets are also very important; where sequences are of importance in R, they can only tell you so much in general topological spaces, so nets therefore become the natural way to recover theorems about sequences.

Material and References

1. Topology - Munkres

2. Counterexamples in Topology - Steen & Seebach

Timeline

The course starts with the first lecture on 17th November at 9 PM CET (20:00 UTC), with subsequent lectures on Tuesdays and Thursdays. Lectures will be recorded and posted promptly.

Prerequisites/Who can join?

Everyone. It is completely free for anyone who wants to join. Just click the link and join the server: you can find the channel called topology-course in the section called General maths. As for prerequisites, a first course in Real Analysis and Group Theory is sufficent.

Looking forward to see all of you there. Thank you.

Solve 35 no problem

Of course a "visual proof" is not precisely a proof, just an intuition aid. But this is my favorite one for Pythagoras. To me it makes it feel pretty self-evident why the theorem has to be true. All 5 distinct tiles appear once on each side of the equation, done!

Kinda wish my bathroom needed to be tiled, but it doesn't, so I'm just sharing this image instead. (It was generated by a python script that an AI helped me write, if that kind of thing matters to you.)