NCERT Solutions for Class 5th Maths Chapter 11 The tile-and-die game: build up to a perimeter of 24 and win — Let Us Play
Book page 154 Updated on2026-09-19
Q1.
Take some square tiles and a die and play the game in pairs. Roll the die and pick the number of tiles equal to the dots on the die. Arrange them to make a shape or figure. (How is the game played?)
Answer
Two players share one tiled figure and take turns adding tiles to it until its perimeter reaches 24. Whoever makes it 24 wins.
What you need: a handful of equal square tiles (cut them from card, 2 cm by 2 cm) and one die.
Player 1 rolls the die. Suppose it shows 4.
Player 1 takes that many tiles — here 4 tiles — and arranges them into one joined figure. Every tile must touch another tile along a full side, not just at a corner.
Both players find the perimeter of the figure by counting the 1-unit sides all the way round the outside.
Player 2 rolls next and adds that many tiles to the same figure. The tiles already on the table are not moved.
Keep taking turns. The player whose tiles bring the perimeter to exactly 24 wins the game.
Where the skill lies: The number of tiles is decided by the die, but the shape is your choice. Spreading the tiles out in a long line makes the perimeter grow fast. Packing them into a block makes it grow slowly. Choosing the arrangement is how you steer the perimeter towards 24.
Rule to remember: Tiles must share a whole edge. Two tiles touching only at a corner do not count as joined.
Q2.
Find the perimeter of the tiles.
The tiles the first player has put down. Each side of a tile is 1 unit long.
Answer
Perimeter = 10 units. The book's answer, = 10, is correct.
Start at the top-left corner of the figure.
Go right along the top: 3 sides. Count 1, 2, 3.
Come down the right end: 1 side. Count 4.
Go left along the middle ledge: 2 sides. Count 5, 6.
Come down the little step: 1 side. Count 7.
Go left along the bottom: 1 side. Count 8.
Climb back up the left edge: 2 sides. Count 9, 10. You are back where you started.
Perimeter = 3 + 1 + 2 + 1 + 1 + 2 = 10 units
A quicker way to check: 4 separate tiles would have 4 × 4 = 16 sides. Here 3 joins were made, and each join hides 2 sides. 16 − (3 × 2) = 16 − 6 = 10. Same answer.
Careful: Count only the sides on the outside. The lines where two tiles meet are inside the figure and are not part of the border.
Q3.
Do not move the tiles. The second player can take turn and add tiles to the same tiled figure. (The die shows 1 and one tile is added — what is the new perimeter?)
The same figure after one more tile was added on top.
Answer
The new perimeter is 12 units. The book's answer, = 12, is correct.
One extra tile was added on top. The perimeter went up by 2.
The die showed 1, so the second player takes 1 tile.
The tile is added to the same figure — nothing already on the table is moved.
The new tile brings 4 sides with it, but one of those sides is stuck against the old figure.
That one join hides 2 sides — one belonging to the new tile and one belonging to the old figure.
So the perimeter changes by 4 − 2 = 2. 10 + 2 = 12 units.
Old perimeter = 10 units New tile adds 4 sides, join hides 2 sides Change = 4 − 2 = +2 New perimeter = 10 + 2 = 12 units
The useful rule of this game: A tile joined along one side adds 2 to the perimeter. A tile tucked into a corner, joined along two sides, adds nothing at all — it hides as much as it brings. A tile in a slot with three sides joined actually reduces the perimeter by 2. Where you place the tile matters as much as how many you get.
Q4.
Take turns and add tiles to the same figure till the perimeter becomes 24. The one who makes the perimeter 24 wins the game. (How can a player reach exactly 24?)
The tiled figure at the end of the game. Each side of a tile is 1 unit long.
Answer
Keep adding tiles along a single edge, because each such tile adds exactly 2 to the perimeter. From 12 you need 6 more such tiles to reach 24.
Count the outside sides one by one — they come to 24.
Know your starting number. After the second turn the figure had a perimeter of 12.
Work out the gap. 24 − 12 = 12 more units of perimeter are needed.
Remember the rule from the last question. A tile joined along one side adds 2. A tile tucked into a corner adds 0.
Divide. 12 ÷ 2 = 6, so 6 tiles placed along one edge each will do it.
Steer with your placing. If you roll a big number and 24 is close, tuck some tiles into corners so they add nothing. If 24 is still far away, stick every tile out on its own edge.
Perimeter needed = 24 units Perimeter so far = 12 units Still to add = 24 − 12 = 12 units Each edge-joined tile adds 2 units Tiles needed = 12 ÷ 2 = 6 tiles
Why you can plan your move: Perimeter never jumps about randomly. Adding one tile changes it by +2, 0 or −2, depending on how many sides you glue down. So before you place a tile, count how many of its sides will touch the figure, and you will know the new perimeter before you let go.
Sample answer: “Our figure had a perimeter of 12. I rolled a 6. I placed all six tiles one after another along the bottom edge, each touching only one side. Each tile added 2, so the perimeter became 12 + 12 = 24 and I won.”