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NCERT Solutions for Class 5th Maths Chapter 4 Let Us Think and Solve — Let Us Think and Solve

Book page 53 Updated on2026-09-19

Q1.
Nitin likes numbers that read the same when read from left to right or from right to left. Such numbers are called palindrome numbers. The numbers 22, 363, 404, and 8,558 are some examples. List all palindrome numbers between 100 and 200. List all palindrome numbers between 900 and 1,200. List all palindrome numbers between 25,000 and 27,000.
Answer

A palindrome number reads the same forwards and backwards, so its first digit must match its last digit, and its second digit must match its second-last digit.

Between 100 and 200 — ten numbers

  1. Every number here starts with 1, so it must also end with 1. The shape is 1 _ 1.
  2. The middle digit can be anything from 0 to 9.
101, 111, 121, 131, 141, 151, 161, 171, 181, 191

Between 900 and 1,200 — twelve numbers

  1. First take the 3-digit ones, from 900 to 999. They start with 9, so they end with 9. The shape is 9 _ 9.
  2. That gives 909, 919, 929, 939, 949, 959, 969, 979, 989, 999 — ten numbers.
  3. Now the 4-digit ones, from 1,000 to 1,200. They start with 1, so they end with 1. The shape is 1 b b 1.
  4. 1001 works and 1111 works. The next one, 1221, is bigger than 1,200, so it is out.
909, 919, 929, 939, 949, 959, 969, 979, 989, 999, 1001, 1111

Between 25,000 and 27,000 — twenty numbers

  1. All these numbers start with 2, so they end with 2. The shape is 2 b c b 2.
  2. The second digit b can only be 5 or 6, because 25 000–25 999 and 26 000–26 999 lie inside the range, while 27 072 and above are outside it.
  3. The middle digit c can be any of 0 to 9. So there are 2 × 10 = 20 numbers.
25052, 25152, 25252, 25352, 25452, 25552, 25652, 25752, 25852, 25952,
26062, 26162, 26262, 26362, 26462, 26562, 26662, 26762, 26862, 26962
Check it yourself: Read 25452 backwards — 2, 5, 4, 5, 2. The same. Read 26762 backwards — 2, 6, 7, 6, 2. The same again.
Q2.
In a 3×3 grid, arrange the numbers 1 to 9 such that each row and each column has numbers in an increasing (inc) order. Each number should be used only once. This time, fill the grid such that each row and column has numbers in decreasing (dec) order.
incincincincincincdecdecdecdecdecdec
Two empty 3×3 grids: in the first, every row and every column must increase; in the second, every row and every column must decrease.
Answer

First grid — every row and every column increasing

123inc →
456inc →
789inc →
inc ↓inc ↓inc ↓

Read across: 1 < 2 < 3, 4 < 5 < 6, 7 < 8 < 9. Read down: 1 < 4 < 7, 2 < 5 < 8, 3 < 6 < 9. Every row and column climbs.

Second grid — every row and every column decreasing

987dec →
654dec →
321dec →
dec ↓dec ↓dec ↓

Read across: 9 > 8 > 7, 6 > 5 > 4, 3 > 2 > 1. Read down: 9 > 6 > 3, 8 > 5 > 2, 7 > 4 > 1. Every row and column falls.

How to build them: Write 1 to 9 in order, three at a time, filling the rows from the top. That automatically makes the rows climb, and it also makes each column climb because every number in a row is 3 more than the one above it. For the decreasing grid, do the same but count down from 9.
There is more than one answer. For example 1, 2, 3 / 4, 5, 7 / 6, 8, 9 also works. There are 42 different ways to fill each of these two grids. Any filling where every row climbs and every column climbs is correct.
Q3.
Now, fill the grids below with numbers (1–9) based on the inc (increasing) and dec (decreasing) conditions, as indicated below. Grid 1: rows dec, dec, dec and columns inc, inc, inc. Grid 2: rows dec, dec, inc and columns dec, dec, inc. Grid 3: rows inc, inc, dec and columns inc, dec, dec.
Answer

Grid 1 — all rows going down, all columns going up

321dec →
654dec →
987dec →
inc ↓inc ↓inc ↓
  1. Rows: 3 > 2 > 1 ✓, 6 > 5 > 4 ✓, 9 > 8 > 7 ✓
  2. Columns: 3 < 6 < 9 ✓, 2 < 5 < 8 ✓, 1 < 4 < 7 ✓

Grid 2 — rows: dec, dec, inc; columns: dec, dec, inc

861dec →
752dec →
349inc →
dec ↓dec ↓inc ↓
  1. Rows: 8 > 6 > 1 ✓, 7 > 5 > 2 ✓, 3 < 4 < 9 ✓
  2. Columns: 8 > 7 > 3 ✓, 6 > 5 > 4 ✓, 1 < 2 < 9 ✓

Grid 3 — rows: inc, inc, dec; columns: inc, dec, dec

168inc →
257inc →
943dec →
inc ↓dec ↓dec ↓
  1. Rows: 1 < 6 < 8 ✓, 2 < 5 < 7 ✓, 9 > 4 > 3 ✓
  2. Columns: 1 < 2 < 9 ✓, 6 > 5 > 4 ✓, 8 > 7 > 3 ✓
A way to find your own answer: Start with the corners. A cell that must be the biggest in both its row and its column is a good home for 9; a cell that must be smallest in both is a good home for 1. In Grid 2 the bottom-right cell has to be the biggest in its row and in its column, so 9 belongs there. Then fill in the rest and adjust.
There are many correct answers. Grid 1 has 42 solutions, and Grids 2 and 3 have 60 each. Check yours by reading every row across and every column down.
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