NCERT Solutions Ganita Prakash (Part 1) Chapter 8 Chess Puzzles — Puzzle Time

Book page 199 Updated on2026-09-05

Q1.
Chess is a popular 2-player strategy game. This game has its origins in India. It is played on an 8 × 8 chequered grid. There are 2 sets of pieces — black and white — one set for each player. Find out how each piece should move and the rules of the game.
Answer

Chess grew out of the ancient Indian game chaturanga. Here is how the six pieces move.

PieceHow it movesNumber per player
King (राजा)One square in any direction1
Queen (वज़ीर)Any number of squares along a row, column or diagonal1
Rook (हाथी)Any number of squares along a row or column2
Bishop (ऊँट)Any number of squares along a diagonal2
Knight (घोड़ा)In an “L”: two squares one way, one square across; it may jump over pieces2
Pawn (प्यादा)One square forward (two on its first move); captures diagonally8

The aim is checkmate — trapping the opponent's King so that it cannot escape capture.

Did you know? The Queen is the strongest piece precisely because it combines the Rook's and the Bishop's moves — which is what makes the puzzle below hard.
Q2.
From its current position, a Queen piece can move along the horizontal, vertical or diagonal. Place 4 Queens such that no 2 queens attack each other.
Answer

On a 4 × 4 board there must be exactly one Queen in every row and every column, and no two on a diagonal.

QQQQ rows 1–4 → columns 2, 4, 1, 3
One valid arrangement of 4 non-attacking Queens on a 4 × 4 board.
Row 1 → column 2
Row 2 → column 4
Row 3 → column 1
Row 4 → column 3
Why it works: all four columns are different, so no vertical attack. For diagonals, check row + column: 3, 6, 4, 7 — all different; and row − column: −1, −2, 2, 1 — all different. Equal sums or equal differences would mean a shared diagonal.
Q3.
Now, place 8 queens on this 8 × 8 grid so that no 2 queens attack each other!
Answer

Again, one Queen per row and per column, with all diagonals clear.

Row12345678
Column15863724
row + column: 2, 7, 11, 10, 8, 13, 9, 12 — all different ✔
row − column: 0, −3, −5, −2, 2, −1, 5, 4 — all different ✔

So no two Queens share a row, a column or a diagonal.

Did you know? The 8-queens puzzle has 92 solutions altogether, but only 12 of them are really different — the rest are rotations and mirror images of those 12.
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