EN हिं

NCERT Solutions Ganita Prakash (Part 1) Chapter 6 The First-ever 4 × 4 Magic Square — In-text Questions

Book page 137 Updated on2026-09-05

Q1.
Chauṭīs means 34. Why do you think they called it the Chautīsā Yantra?
Answer

Because every row, every column and every diagonal of that 4 × 4 square adds up to 34 — so the number 34 is the identity of the yantra.

712114
213811
163105
96154
Rows: 7 + 12 + 1 + 14 = 34,  2 + 13 + 8 + 11 = 34,  16 + 3 + 10 + 5 = 34,  9 + 6 + 15 + 4 = 34
Columns: 7 + 2 + 16 + 9 = 34,  12 + 13 + 3 + 6 = 34,  1 + 8 + 10 + 15 = 34,  14 + 11 + 5 + 4 = 34
Diagonals: 7 + 13 + 10 + 4 = 34,  14 + 8 + 3 + 9 = 34
Why it happens: the square uses the numbers 1 to 16, whose total is 1 + 2 + … + 16 = 136. Spread equally over 4 rows, each row must get 136 ÷ 4 = 34. So 34 is forced.
Did you know? this inscription is from the 10th century Pārśhvanath Jain temple at Khajuraho — the earliest recorded 4 × 4 magic square in the world.
Q2.
Every row, column and diagonal in this magic square adds up to 34. Can you find other patterns of four numbers in the square that add up to 34?
Answer

Yes — this square is extraordinarily rich. Here are patterns that all add to 34:

PatternNumbersSum
The four corners7 + 14 + 9 + 434
The centre 2 × 2 block13 + 8 + 3 + 1034
Top-left 2 × 2 block7 + 12 + 2 + 1334
Top-right 2 × 2 block1 + 14 + 8 + 1134
Bottom-left 2 × 2 block16 + 3 + 9 + 634
Bottom-right 2 × 2 block10 + 5 + 15 + 434
Middle two of the top and bottom rows12 + 1 + 6 + 1534
Middle two of the left and right columns2 + 16 + 11 + 534
A broken diagonal12 + 8 + 5 + 934
Another broken diagonal1 + 11 + 16 + 634
A “kite” shape7 + 8 + 15 + 434
Its mirror14 + 13 + 3 + 434
Why it happens: the Chautīsā Yantra is what mathematicians call a most-perfect magic square. Every 2 × 2 block, and every set of four cells that “wraps around” the edges like a broken diagonal, also totals 34. That is far more than an ordinary magic square promises.
Try This: pick any 2 × 2 block anywhere in the grid, letting it wrap around the sides, and add the four numbers. You will get 34 every single time.
Was this helpful? Report an error