Practical knowledge library

Small Ideas That Solve Real Problems

Find focused programming tips and useful math techniques, then move from the quick answer to a complete course, guide, or practical browser tool.

60Published tips
30Programming
30Mathematics
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Programming tips and math tricks

Each entry starts with the problem, explains the direct solution, and shows why the technique is useful.

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Math

Square Numbers Near 50

Problem

Squaring numbers like 48 or 52 requires long multiplication.

Solution

Use (50-a)² = 2500 - 100a + a² or (50+a)² = 2500 + 100a + a²

Benefit

Converts difficult squares into simple arithmetic around 2500.

Math

Divisibility Rule for 4

Problem

Testing divisibility by 4 for large numbers requires division.

Solution

Check only the last two digits. If they form a number divisible by 4, the whole number is.

Benefit

Instantly test any number for divisibility by 4.

Math

Divisibility Rule for 6

Problem

Checking divisibility by 6 requires checking both 2 and 3 separately.

Solution

Number must be even AND sum of digits divisible by 3.

Benefit

Combines two simple rules for quick divisibility check.

Math Popular

Multiply by 25 Instantly

Problem

Multiplying by 25 requires complex long multiplication.

Solution

Divide by 4 and multiply by 100 (or multiply by 100 and divide by 4).

Benefit

Converts multiplication into simple division by 4.

Math

Day of Week Algorithm (Mental Calendar)

Problem

Figuring out what day of the week a date falls on requires a calendar.

Solution

Use Zeller's congruence simplified: Learn anchor days for each month and count forward/backward.

Benefit

Impress others by calculating any date's day of week mentally.

Math

Compound Interest Rule of 72

Problem

Calculating how long it takes for investment to double requires complex formulas.

Solution

Divide 72 by the interest rate to get approximate years to double.

Benefit

Quick investment doubling time calculation without formulas or calculators.

Math

Estimate Cube Roots

Problem

Finding cube roots mentally is extremely difficult.

Solution

Memorize cubes 1-10, then find which two cubes the number falls between.

Benefit

Estimate cube roots within ±0.5 by knowing 10 reference points.

Math Popular

Percentage Increase/Decrease Formula

Problem

Calculating percentage change between two values is confusing and error-prone.

Solution

((New - Old) / Old) × 100. Positive = increase, negative = decrease.

Benefit

Universal formula for all percentage change calculations.

Showing 17-24 of 30 tips

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