NCERT Solutions for Class 7th Maths Chapter 1 Puzzle Time
Updated on2026-09-19
Q1.
Draw lines and split the region consisting of white squares into 6 smaller congruent regions.
Answer
The grid is 5 × 5, and the green square in the middle is not part of the region.
Total small squares = 5 × 5 = 25 White squares = 25 − 1 = 24 24 ÷ 6 = 4 squares in each region
So each of the six pieces must be made of 4 squares, and all six must be the same shape. An L-shaped piece of 4 squares works. Here is one way to do it — the six pieces are shown in six colours.
Six congruent L-shaped pieces of 4 squares each. The green square in the centre is left out.
Every piece is the same L of 4 squares — three in a row with one more square turned at the end. The pieces are only rotated, never made bigger or smaller, so all six are congruent.
Why it happens: first count. Six equal pieces out of 24 squares means 4 squares each, which cuts down the shapes worth trying. A straight piece of 4 will not work, because the squares next to the hole cannot be reached by one; the L bends around the hole neatly. Notice that the finished pattern has half-turn symmetry — turn the picture upside down and piece 1 lands on piece 6, piece 2 on piece 4, and piece 3 on piece 5.
Try This: take out a corner square instead of the middle one and try again with six pieces of 4 squares. Does an L still work?