# Tag Info

Accepted

### Patrick and Rachel go to a tennis tournament with 7 other couples

First notice the wording of the question: "Patrick asked everyone how many people they played against, and found that each one answered with a different number" This means that In ...
• 123k

### Find all solutions to a sum of fractions

Solutions Reasoning
• 123k

### Elegant solution to this digit puzzle

Solutions: Explanation:
• 915

### Some doctors and a lot of hand shakes

Every hand shake that occurs Since Group O
• 5,178

### Show there is always a pair at least 16 apart

Perhaps I'm missing something but here is a quick proof
• 123k
Accepted

### Tiling twelve 5 x 10 rectangles with ten sets of the twelve pentominoes

It is easier to halve the size of the puzzle - using 5 sets of pentominoes to cover 6 of those rectangles. If that can be solved, you can simply use two copies of that as a solution. I'll restrict ...
• 43.1k

### Can the Spider catch the Fly?

Assumption (& simplification): The spider and the fly starts at different finite points on an infinite 1-d axis. Furthermore, assume the fly starts somewhere. Whether it's 10, 100 or 1000 it ...
• 2,689

### Elegant solution to this digit puzzle

Overall, I've counted so there will inevitably be some degree of case bashing. This is how I would proceed. Notice firstly that Suppose $f < 9$ Now suppose $f=9$
• 123k

### Some doctors and a lot of hand shakes

This seems pretty straightforward:
• 3,683

• 3,450
Accepted

• 264

### Mice and their relations

This seems quite straightforward.
• 43.1k

### What size square grid can you tile?

I'll generalise it slightly to ask what $m\times n$ grids can be tiled. The tile has area $4$, so clearly we need $mn$ to be divisible by $4$.
• 43.1k
Accepted

### Bertrand's Ballot Theorem

Let $y$ be the current number of votes for $B$, and $x$ be the number of current votes for $A$. If $y>x$ at any time, then $x=y$ at some point in this count. So we have to find the probability that ...
• 56

### Good Rectangles and Evil Numbers

So it is proved that only the following set might be evil I wrote an MIQCP model and solved with gurobi for the remaining numbers, proving they are truly unfeasible and so evil. (My model can only ...
• 486
Accepted

### A strange corporate

I came up with: Rationale: Double checked myself in Excel, and discovered that I should have finished my handwritten version. And for the bonus question:
• 1,211

### Elegant solution to this digit puzzle

I just wanted to 'see' what the solutions looked like, but I disqualified myself by using a computer to get the solutions. Anyway, here is a visualization for your amusement. Visualization ...
• 2,213

### How high does the ladder reach up the wall?

Let h,w be the height and width of the triangle formed by the ladder with the wall and the ground. First let us divide through with d: $H:=h/d, W:=w/d, L:=l/d, D:=d/d=1$ Then $L^2=H^2+W^2$ (1). ...
• 11.6k
Accepted

### Productive Neighbours

A solution by hand: Now that it's known which digits fall in each loop, the exact placement is straightforward.
• 1,075

### A barrel contains 10l of whiskey, another one contains 10l of coca-cola. If I do the following operation

Never mind any of the transfer operations: the amount of whiskey in the cola barrel will be This is enough to tell us that whenever there's an equal amount of liquid in both barrels, the amount of ...
• 68.2k
Accepted

### Will Romeo meet Juliet?

Let $R$ and $J$ be uniform $[0,1]$ random variables to represent the arrival times of Romeo and Juliet, respectively. The star-crossed lovers meet if $|R-J|\le 1/4$. The desired probability is the ...
• 7,429
Accepted

### How many colleagues went to Starbucks?

If you have $25$% of the total coffee and $50$% of the total milk: Using this, we find: So there are:
• 1,954

### Can the Spider catch the Fly?

Yes, the spider can always catch the fly. First, observe a simpler case: Now, let the start distance to be unknown:
• 650
Accepted

### A bunch of circles and squares

Original Partial Answer (Complete Answer below this one): Weeks ago I figured out that the gray section "IN" means thinking that the values in order are At first I thought the slopes of ...
• 13.1k
1 vote

### Productive Neighbours

The unique placement is where x = Here is my thinking: Then I had the idea to brute force it, so I Then, I named each region in the diagram a letter from A-G and added a few columns to calculate ...
• 13.1k
1 vote

### Good Rectangles and Evil Numbers

The evil numbers are as already stated by @xd y . What this post adds is a simple non computer aided proof: a) these are really bad: Given a tile t and an x offset we say t covers x if there is a y ...
• 11.6k

Only top scored, non community-wiki answers of a minimum length are eligible