XOR, also known as Exclusive OR, is a logical operation often used in programming. It is referred to $\oplus$, but in programming, for simplicity, it is referred to as $^$. There are many special propreties about XOR: The order in which you calculate XOR operations does not matter, for example, $2^3^1^4$ can also be calculated […]
Year: 2026
Telescoping
A telescoping sum is a sum that is calculated when immediate terms cancel out. For terms like $\frac{1}{n(n + k)}$, it equals $\frac{1}{k}(\frac{1}{n} – \frac{1}{n + 1})$. A special case, 1, must be noted. Everything simplifies to $\frac{1}{n} – \frac{1}{n – 1}$ There are also other telescoping formulas, like General Linear Denominator and Radical Telescoping […]
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There will be more coming tomorrow so stay watchful!
Flavours of Cake
These are all the flavours of cake I could think of, and if I missed any, please let me know. Also, I did not search up anything, my list is entirely from memory. Chocolate cake Vanilla cake White cake Black velvet cake Red velvet cake Banana cake Marble cake Zebra cake Pineapple upside-down cake Pound […]
Distance Preserving Proprety of Rotation
Rotation is a transformation in metric spaces. Though the positions of points and lines will change, their lengths and angles will not. A rotation is a type of isometry that moves all points according to a fixed point known as the rotocenter.
Reducution Efficiency
When you see a large fraction, always reduce with the largest factor first. For example, What is the value of this expression in decimal form? Obviously, this is divisible by 2, but we can do better than that. Did you notice that all of them are divisible by 11? If we reduced by 2, we […]
Always Read the Question!
Always read the question! For example: Find the ones digit of 222222-22222-2222-222-22-2. If you don’t read the question first, you might just calculate the whole thing. But if you did, you could just look at the ones digits. It saves a lot of time.
How to Make Antique-Style Paper
In this post, I will explain how to make antique-style paper. First, brew 4 tablespoons of strong coffee. It may be decaf. If you would like a more fragile paper, increase the water content. If you would like a stiffer paper, decrease the water content. Next, take two sheets of blank paper. I like to […]