New NCERT Ganita Prakash Part 2 · Class 8 Maths · Part II · Chapter 6: Algebra Play
This chapter uses algebra to explain number tricks and puzzles. It covers think-of-a-number tricks, number pyramids, calendar grids, divisibility tricks and how to solve word puzzles by forming equations.
From the Class 8 Maths Formula Sheet, made as per the new NCERT book Ganita Prakash · Pages 53–56 of the book.
Key points
- Algebra explains why a trick always works: write the steps with a letter and simplify.
- In the classic trick x → 2x → 2x + 4 → x + 2 → (x + 2) − x, the answer is always 2.
- In the date trick, the result is 100M + 165 + D; subtract 165 to get the month and day.
- For digits p < q < r, the largest 2-digit × 1-digit product is qp × r.
- In a number pyramid, each brick is the sum of the two bricks below it.
- In a 2 × 2 calendar block a, a + 1, a + 7, a + 8, the sum is 4a + 16.
- Reversing a 2-digit number and subtracting always gives a multiple of 9; adding gives a multiple of 11.
- Writing a 3-digit number twice (abcabc) gives a multiple of 7, 11 and 13.
- To solve a puzzle: let the unknown be a letter, write each fact as an expression, form an equation, solve and check.
- Virahanka described the sequence 1, 2, 3, 5, 8, 13 … long before Fibonacci.
Formulas
| Date trick result | 100M + 165 + D M = month, D = day |
| 3-row number pyramid | top = a + 2b + c |
| 4-row number pyramid | top = a + 3b + 3c + d |
| 2 × 2 calendar block sum | a + (a + 1) + (a + 7) + (a + 8) = 4a + 16 |
| Calendar diagonal products | (a + 1)(a + 7) − a(a + 8) = 7 |
| Reverse and subtract | (10b + a) − (10a + b) = 9(b − a) |
| Reverse and add | (10a + b) + (10b + a) = 11(a + b) |
| abc + bca + cab | 111(a + b + c) = 3 × 37 × (a + b + c) |
| Write abc twice | abcabc = abc × 1001 = abc × 7 × 11 × 13 |
| Largest product comparison | qp × r = 10qr + pr > rp × q = 10qr + pq since r > q |
Diagrams to learn
- A 3-row number pyramid: top = a + 2b + c
- A 2 × 2 block on a calendar
- Table decoding divisibility tricks with algebra
- Date trick results table
- Algebra explains why a trick always works: write the steps with a letter and simplify.
- In algebra grids, find the row with only one kind of shape first, then substitute and solve the next row.
- Always check the answer in the story after solving the equation.
A real page from the book
Get the full chapter in the book
This page is a summary. The Class 8 Maths Formula Sheet has the complete chapter in colour, with every diagram and worked example.
Frequently asked questions
How does the date trick work in Algebra Play?
Multiply the month M by 5, add 6, multiply by 4, add 9, multiply by 5 and add the day D. The result is 100M + 165 + D, so subtracting 165 shows the month and day.
Why is a 2-digit number minus its reverse always divisible by 9?
(10b + a) − (10a + b) = 9(b − a), which is always a multiple of 9. For example, 74 − 47 = 27.
What is the top of a 3-row number pyramid?
If the bottom row is a, b, c and each brick is the sum of the two below it, the top is a + 2b + c.
← Part II · Chapter 5: Tales by Dots and LinesPart II · Chapter 7: Area →
