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NCERT Solutions for Class 7th Maths Chapter 4 Puzzle Time

Updated on2026-09-19

Q1.
Try solving the following Hidato puzzles. Puzzle 1: a 5 × 5 grid with 25 in the top-left corner, 1 in the top row third cell, 20 and 4 in the second row, 14 and 8 in the third row, 15 and 9 in the fourth row.
Answer

Here is the completed grid.

2523123
24202254
19142186
18131579
1716121110

(The orange numbers are the ones printed in the book.)

How to get there:

  • The grid has 25 cells and the numbers run from 1 to 25, so every cell is used exactly once.
  • 1 is fixed in the top row and 4 in the last column, only three steps away. The run 1 → 2 → 3 → 4 therefore hugs the top-right corner.
  • From 4 the chain must come back down: 5, 6, 7 fill the right-hand block around the given 8 and 9.
  • 10, 11, 12 run along the bottom row, and 13 must sit next to the given 14.
  • 15 is fixed, so 16 and 17 finish the bottom-left corner and 18, 19 climb the first column to reach 20.
  • 21 and 22 fill the middle column, and 23, 24 lead into 25 in the corner.
Why the count matters: in a Hidato the path visits every cell, so the largest number is always equal to the number of cells. Counting the cells first tells you the highest number even before you start — and it is the quickest way to check a grid.
Note on the worked example on page 95: two cells of the printed Solution grid carry wrong numbers. The cell to the left of 26 should be 29 (it is printed as 39, but 39 already appears above it), and the cell to the right of 7 in the second-last row should be 6 (it is printed as 16, but 16 already appears). With those two corrections the path runs 1, 2, 3, … 40 without a break.
Q2.
Puzzle 2: the seven-row grid with holes, carrying the clues 36, 1, 2 in the top row, 4, 6, 13 in the second, 34 and 12 in the third, 39 and 30 in the fourth, 31 in the fifth, 17 in the sixth and 26, 23, 21 in the last.
Answer

This puzzle cannot be completed as it is printed — and counting shows why.

Cells in the printed grid, row by row:
5 + 7 + 6 + 4 + 3 + 5 + 7 = 37 cells

Highest number given (the circled clue) = 39

A Hidato path visits every cell exactly once, so the highest number must equal the number of cells. Here 39 ≠ 37, so no filling can work. Two cells appear to have been dropped from the printed grid.

What you can still work out:

  • The cell holding 39, on the left of the fourth row, touches only one other cell — the cell directly above it. A cell with a single neighbour must be an end of the path. Since 39 is the largest clue, that cell is indeed the finish, and 38 must sit directly above it.
  • The cell holding 1 is the other end of the path, and 2 is already printed beside it.
  • 2 is printed next to 1, and 4 and 6 are printed in the second row, so 3 must be one of the cells touching both 2 and 4, and 5 one of the cells touching both 4 and 6.
  • The clues 12, 13 next to each other, and 21, 23, 26, 30, 31, 34, 36 spread out, show the path sweeping down the right side, back along the bottom and up the left.
Why the count argument settles it: the numbers 1, 2, 3, … 39 are 39 different numbers, and each needs its own cell. With only 37 cells, two numbers would have nowhere to go. This is a good habit for every puzzle in the family — count the cells before you write anything.
Tip: do not spend long hunting for a filling that does not exist. Instead, redraw the grid with 39 cells — keeping the clues where they are — and solve that. Or simply renumber the puzzle for 37 cells and see how far the clues take you. Either way, the method is the one used in Puzzle 1: start from the cells with the fewest neighbours.
Q3.
Puzzle 3: the large cross-shaped grid of 56 cells with 56 circled at the left, 1 circled in the middle, and the clues 9, 7, 10, 5, 17, 15, 44, 49, 28, 54, 42, 50, 29, 26, 35, 34, 25, 23 and 39.
Answer

The grid has exactly 56 cells and the numbers run 1 to 56, so every cell is filled. Here is the completed grid (dots are cells outside the shape).

····89····
····710····
··4611121314··
··53211715··
·4546474831161819·
·4443493230282720·
55544251503329262421
56535241363534252322
····4037····
····3938····

(The orange numbers are the ones printed in the book.)

How to get started:

  • Count the cells: 2 + 2 + 6 + 6 + 8 + 8 + 10 + 10 + 2 + 2 = 56, which matches the circled 56. Good — the puzzle is sound.
  • The two thin arms at the top and the bottom hold only two cells each, so the path must go in and come straight back out. The clues 7, 9, 10 sit in the top arm, and 39 in the bottom arm, which fixes 8 above 7 and pins 37, 38, 40 around 39.
  • 1 and 5 are both given, with only three cells between them, so 2, 3 and 4 must fill that short stretch of the fourth row and the cell just above it.
  • 15 and 17 are printed side by side, so 16 must be a cell touching both of them — and the row below is the only place with room for the numbers that follow.
  • 26, 28 and 29 are printed close together; 27 has to be the one cell that touches both 26 and 28.
  • Work outwards from each such forced cell. The corners of the arms and the single-neighbour cells always give the firmest footholds.
Why the puzzle has only one answer: the given numbers are placed so that at every stage some cell has just one possible value. Each fixed number cuts the choices for its neighbours, and the chain of forced steps runs all the way from 1 to 56. That is the point of the pre-filled clues the book mentions.
Check it yourself: trace 1, 2, 3, … 56 with a finger. Each step should move to a cell that touches the last one — sideways, up and down, or corner to corner — and no cell should be left empty.
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