Algebra Play — Interactive Lab

6.2 Think of a Number

Pick any starting number. Double it, add a constant K, divide by 2, then subtract the original number — no matter what you started with, you always land on K/2!

Think of a number (x): Add this constant (K):

I want the final answer to be:

The algebra: 2x + K, then divide by 2 → x + K/2, then subtract x → K/2. The x always cancels out, so the final answer only depends on K — never on your starting number!

Think of a Date

Pick a month (M) and day (D). Follow the steps below — then use the reverse calculator to guess the date back from just the final answer, exactly like Shubham does to Mukta!

Month (1–12): Day (1–31):

Guess the Date (reverse it!)

Final answer told to you:

Algebra: final = 100M + 165 + D. Subtract 165, and the last two digits of what's left are D, while what remains before that is M.

6.3 Number Pyramids

Each number is the sum of the two directly below it. Edit the bottom row and watch the whole pyramid — and the algebraic formula for the top — update live.

Number of rows:

Top value = —

Formula (coefficients from Pascal's triangle) = —

Try filling the bottom row with the first few Virahāṅka-Fibonacci numbers (1, 2, 3, 5, 8, …) — is the number at the top also a Fibonacci number?

6.4 Fun with Grids — Calendar Magic

Click a date to select the top-left corner of a 2×2 block. The sum of the 4 dates always equals 4a + 16, where a is the top-left date — try it, then use the reverse calculator to find the block from just its sum!

Selected block sum = —

4a + 16 check = —

Given sum:

a = (sum − 16) / 4. If this isn't a whole number valid for the calendar, no such block exists!

Algebra Grids — Shapes as Unknowns

Each row gives an equation: so many of shape A plus so many of shape B equals the row's total. Enter two rows to solve for A and B, then use a third row to predict its total.

Row 1 — count of A: count of B: Row 1 total: Row 2 — count of A: count of B: Row 2 total:

Value of A = —

Value of B = —

Row 3 — count of A: count of B:

Predicted Row 3 total = —

6.5 The Largest Product

Enter three different digits. See every way of arranging them as (2-digit) × (1-digit), and which arrangement gives the biggest product.

Digit 1: Digit 2: Digit 3:

6.6 Decoding Divisibility Tricks

Reverse & Subtract → Always Divisible by 9

2-digit number (distinct digits):

Reverse & Add → Always Divisible by 11

2-digit number:

Cyclic 3-Digit Sum → Always Divisible by 37

3-digit number abc:

Repeat-the-Digits Trick (÷7, ÷11, ÷13)

3-digit number abc:

Algebra Word Problem Calculators

Horses & Hens (heads & legs)

Total heads: Total legs:

Horses = —

Hens = —

Mother & Daughter Ages

Mother is (×) times daughter's age now: In this many years: Mother will be (×) times daughter's age then:

Daughter's age now = —

Gauri & Naina's Cows

Naina has (×) times Gauri's cows: Cows Naina would give Gauri to equalise:

Gauri's cows = —

Naina's cows = —

Dosa Cart Pricing

Daily rent (₹): Cost per dosa (₹): Desired profit (₹): Dosas sold per day:

OR — price customers will pay (₹):

Required price = —

Dosas needed = —

Karim and the Genie

Each round: coins double, then the genie takes a fixed cost c. After n rounds, coins left = 2ⁿ·x₀ − c·(2ⁿ−1).

Cost per round (c): Number of rounds (n): Coins left after n rounds:

Initial coins = —

Initial coins (x₀): Number of rounds (n):

Required cost per round = —

This is the cost c that drives the final coin count to exactly 0.