NCERT Solutions for Class 5th Maths Chapter 1 King's Horses — King's Horses
Book page 15–16 Updated on2026-09-19
Q1.
But wait, were there really 20 horses in the stable? Count the horses one by one and check!
Answer
No. There were only 19 horses. One had already been stolen.
The stable is a square ring of 12 rooms — 4 rooms along each wall, with an open yard in the middle. Here is exactly what the picture in the book shows.
The stable as the caretaker arranged it. Count the dots: 19 horses in all.
Top side : 1 + 2 + 2 + 0 = 5 Right side : 0 + 2 + 3 + 0 = 5 Bottom side : 0 + 2 + 3 + 0 = 5 Left side : 1 + 1 + 3 + 0 = 5
Every side really does have 5 horses. And yet the total is 19, not 20.
Q2.
What was the mistake in the caretaker's explanation?
Answer
The caretaker counted the corner rooms twice.
Step 1 — see which rooms belong to two walls. The four rooms at the corners of the square sit on two walls at once. A corner room is part of the top wall and the left wall, for example.
The four yellow rooms are corners. Each one sits on two walls, so each is counted twice when you go round the square.
Step 2 — see what that does to the count.
4 sides × 5 horses = 20 counts But the corner horses got counted twice. The corner rooms hold 1 + 0 + 0 + 0 = 1 horse. 20 – 1 = 19 horses ✓
The idea to remember: Going round a square, the four sides share their end rooms. So sum of the four sides is not the same as total number of horses — it is the total plus the corners, counted one extra time. That is exactly the gap the caretaker hid in.
Try This: Draw a square of 12 chairs and put one child on each corner chair. Walk round counting side by side, then count the children directly. The difference will be 4 — one for each corner.
Q3.
The following night, the thief stole another horse from the stable. Now, only 18 horses remained. The caretaker once again cleverly arranged the 18 horses, so that there were 5 horses on each side of the square stable. How do you think he was able to do it? Arrange the 18 horses in the stable with 5 on each side.
Answer
He moved more horses into the corner rooms. The more horses sit in corners, the more often they get counted twice, and the fewer horses he needs in total.
Here is one arrangement of 18 horses with 5 on every side.
18 horses, 5 along every side. The two top corners now hold 1 horse each.
Sum of the four sides = total horses + horses in the corners 4 × 5 = 18 + corners 20 = 18 + corners → corners must hold 2 horses
In our picture the corners hold 1 + 1 + 0 + 0 = 2 horses. ✓ Yesterday, with 19 horses, the corners held only 1.
Try This: Find a different arrangement of 18. Any layout whose four corner rooms hold 2 horses altogether, with 5 on each side, will do.
Q4.
How many more horses can the thief steal before the king notices something is wrong? Try making the arrangements yourself.
Answer
8 more horses. The caretaker can keep up the trick until only 10 horses are left.
Step 1 — write down the rule again.
4 sides × 5 = total horses + horses sitting in corners 20 = total + corners So : total = 20 – corners
Step 2 — to make the total small, make the corners big. So put as many horses as possible in the four corner rooms, and none anywhere else.
Step 3 — how big can the corners get? Each side has 5 horses, and if the two middle rooms of that side are empty, both corners of that side must add to 5. Going round the square, the corners must be 3, 2, 3, 2.
Horses now = 18 Fewest possible = 10 18 – 10 = 8 more horses can be stolen
Why the trick stops at 10: Once the corners are as full as they can be, there is no more double-counting left to hide behind. Take away one more horse and some side will have only 4, and the king will see it.
Try This: Make the in-between arrangements too. 17 horses need 3 in the corners, 16 need 4, 15 need 5, and so on — right down to 10 horses needing 10 in the corners.