NCERT Solutions for Class 2 Joyful Maths Chapter 11 Puzzle

Question B. Complete the pattern.
Answer: The pattern shows:
2 + 2 = 4
+       +
1
1 + 3 = 4

The missing numbers are: 2 (in the first row, second box) and 3 (in the second row, last box).
In simple words: Fill in the missing numbers so that both rows add up to the same answer. The top row needs a 2, and the bottom row needs a 3.

Exam Tip: Check your work by adding across and down to make sure all sums match the target numbers shown.

Question A. Draw lines to connect each pair of similar shapes together. The lines must not cross or touch each other and do not use diagonal lines.
Answer: Match each shape by drawing non-crossing horizontal and vertical lines only. Stars connect to stars, rectangles to rectangles, circles to circles, and triangles to triangles. The solution shows all six pairs linked without any lines crossing or touching one another.
In simple words: Draw paths using only up, down, left, and right moves - no diagonal or crossing lines. Connect shapes that look the same.

Exam Tip: Start with the shapes that are furthest apart, then work inward - this helps avoid getting stuck with crossing lines later.

Question C. Think and complete.
Answer: The pattern transforms a square into a circle by the same process that changes a star into a filled circle with a pattern. The second blank should be filled with option (c) - a filled circle with small dots.
In simple words: A square becomes a circle. A star becomes a circle with dots inside, just like the first pair.

Exam Tip: Look for what changes between the first and second shapes in each row - the same change happens in the blank space.

Question C. Think and complete.
Answer: The letter c is the 3rd letter of the alphabet, which matches the number 5. The letter e is the 5th letter, which matches 9. The number 7 matches the letter g, which is the 7th letter.
In simple words: Each letter's position in the alphabet tells you the answer. Letter c is number 3 in order, e is number 5, and g is number 7.

Exam Tip: Count through the alphabet carefully - a is 1, b is 2, c is 3, and so on. Some letters pair with numbers that are double or more than their position.

Question D. Find the number.
Answer: Start with 10. Double it to get 20. Add 8 to get 28. Take half of 28, which is 14. Subtract the number you started with (10) to get 4. Yes, the answer is 4. Try this trick with your friends using any starting number, and you will always get 4 as your final answer.
In simple words: Pick any number, double it, add 8, divide by 2, then subtract your starting number. You always end up with 4.

Exam Tip: This trick works because the doubling and halving cancel each other out, leaving you with just half of 8, which is always 4.

Question E. Look at the picture. How many different ways can the ant return to its home (anthill)?
Answer: There are 6 different paths the ant can take to get back to its home. The answer diagram shows all six possible routes marked with dashed pink lines going from the starting position to the anthill, each taking a different path through the grid while avoiding obstacles.
In simple words: The ant can walk home in 6 different ways. Each path goes around the grid differently to reach the hill.

Exam Tip: Count carefully by tracing each separate path from start to finish - make sure no two paths are the same.

Question F. Find the number names from 11 to 20.
Answer: The number names eleven through twenty are hidden in the word search grid. They are highlighted and circled in the solution: eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen, and twenty can all be found reading across, down, or diagonally in the letter puzzle.
In simple words: Search the grid to find and circle all ten number words from eleven to twenty. They hide in rows, columns, and sometimes diagonally.

Exam Tip: Work through the alphabet grid row by row, and keep a list of which numbers you have found so you do not search for the same one twice.

Question G. Identify the appropriate shadow image.
Answer: The correct shadow is the one shown in the circle - a dark silhouette of the yellow bug with the antennae and legs in the exact same shape and position as the original picture.
In simple words: The shadow must match the bug's outline perfectly - same shape, same size, same pose.

Exam Tip: Look at the outline of the main picture carefully - count the legs, antennae, and bumps to find the exact match among the shadow choices.

Question H. In how many different ways can the cat return to its house?
Answer: The cat can return to its house in 3 different ways. The three paths are shown as numbered routes (①, ②, ③) in the answer diagram, each offering a separate direction from the cat's starting spot to the house entrance.
In simple words: There are 3 different paths marked on the grid. Each one takes the cat home by a different route.

Exam Tip: Trace each path from the cat to the house carefully - count how many separate routes exist without retracing any steps.

Question I. Try to make two squares by removing two matchsticks.
Answer: Remove two matchsticks to form two separate squares. One way to do this is to take away two sticks from the middle, leaving a small square on the left and a small square on the right, with the remaining sticks arranged to form these two distinct squares as shown in the answer diagrams.
In simple words: Take away 2 sticks so that you have exactly 2 separate squares left behind.

Exam Tip: Try removing sticks from different positions and count the squares that remain - sometimes removing from the middle works better than removing from the edge.

Question J. Who am I?
Answer: Circle.
In simple words: I am round and found in bicycles, cars, and buses - I roll, and nothing moves without me.

Exam Tip: Read each clue carefully - the word "flat" is a big hint that this object cannot work when it loses its shape.

Question K. Which balls will you select to make a total of 30?
Answer: Select the balls marked 11, 4, and 15 to make a total of 30. These three balls add together as 11 + 4 + 15 = 30, as shown circled in the answer grid.
In simple words: Pick the three balls that add up to exactly 30. The ones you want are 11, 4, and 15.

Exam Tip: Add different combinations of three numbers from the grid until you find a set that totals exactly 30 - write down each attempt so you do not repeat yourself.

Question L. Make two different two-digit numbers by using only one digit.
Answer: You can make 11, 22, 33, 44, 55, 66, 77, 88, and 99 - these are all two-digit numbers where the same digit repeats in both the tens place and the ones place.
In simple words: Write a digit twice to make a two-digit number where both digits are the same - like 11, 22, or 33.

Exam Tip: Use digits 1 through 9 - each one can be doubled to make a valid two-digit number following this pattern.

Question M. Draw a path so that hungry giraffe can reach the tree.
Answer: A pathway is drawn through the maze with a red dashed line, showing the giraffe a route from the starting point at the top left to the tree at the bottom right. The solution path navigates around the walls and dead ends to reach the goal successfully.
In simple words: Draw a line from the giraffe at the start to the tree at the end, moving only through open spaces and not crossing any walls.

Exam Tip: Trace the maze slowly from start to finish - mark any dead ends you find so you do not try the same wrong path twice.

Question N. Look at the above picture and write the answers.
(i) Name the animal whom giraffe met first on the path?
(ii) Name the animal whom giraffe met in the last?
(iii) Have you ever lost your way to home?
(iv) What do you do to remember your way to home?
Answer:
(i) Cat
(ii) Bird
(iii) Never
(iv) I remember the landmarks.
In simple words: The giraffe saw a cat at the beginning of the journey and a bird at the end. When you travel, remember special buildings and spots to help you find your way home.

Exam Tip: Read each question carefully before answering - look at the picture and trace the giraffe's path in order to identify each animal correctly.

Question O. How many rectangles can be made after joining the dots given below?
Answer: 9 rectangles can be made. The solution shows nine different rectangles formed by connecting the dots in various ways - some are small individual rectangles, some are combinations of smaller rectangles joined together, and one is a square (which is a special type of rectangle, as noted in the hint).
In simple words: By connecting different dots together, you can draw 9 shapes that are rectangles or squares. Squares count as rectangles too.

Exam Tip: Count small single rectangles first, then look for larger rectangles made by combining smaller ones - remember that squares are special rectangles and must be included in your count.

Question P. Complete these by using addition or subtraction of numbers.
Answer: For the first hexagon with center 9: the outer sections show 18 - 9 = 9, 21 - 9 = 12, 10 - 1 = 9. For the second hexagon with center 13: the outer sections are 11 + 2 = 13, 16 - 3 = 13. For the third hexagon with center 19: the outer sections are 25 - 6 = 19, 16 + 3 = 19.
In simple words: Each number on the outer edge either adds or subtracts to equal the center number. Fill in the missing numbers to make each equation work.

Exam Tip: Look at the pattern of operations around each hexagon - some sides use addition while others use subtraction, so check each one separately.

Question Q. A shepherd has 4 sheep and 4 dogs. Divide the garden into 4 areas, such that each portion or area contains one tree, one sheep and one dog.
Answer: The garden is divided into four sections by drawing lines that separate it into four equal areas. Each section contains exactly one tree, one sheep, and one dog, as required by the puzzle. The answer diagram shows these four distinct portions clearly marked within the oval garden shape.
In simple words: Draw lines to make 4 separate areas. Put 1 tree, 1 sheep, and 1 dog in each area so everything is divided equally.

Exam Tip: Count the total items (4 trees, 4 sheep, 4 dogs = 12 items for 4 areas), and plan your lines so each area gets exactly 3 items - one of each kind.

Question R. Who am I? (A mirror can help you)
Answer:
(i) 54
(ii) 83
(iii) 69
(iv) 71
In simple words: When you look at these numbers in a mirror, they flip and show you different numbers. The upside-down versions are what you read in the mirror's reflection.

Exam Tip: Hold a mirror next to each number or rotate it upside down mentally - digits like 2, 5, and 9 look like other numbers when reversed (2↔5, 6↔9).

Question S. How will you arrange the numbers 1 to 7 so that the three arms have the same total?
Answer: Arrange the numbers in a three-armed pattern where the center circle holds 1, and the three arms extend outward. The arrangement is: center 1, then going along the three arms place 7 at the top, 2 below it, then 4, 3, 5 continuing on the middle arm, and 6 on the bottom arm. Each of the three arms totals to the same value when you add the numbers along that arm.
In simple words: Put number 1 in the middle. Place 7, 2, 6, 4, 3, 5 on the three arms so all arms add up the same way.

Exam Tip: Find a center number that allows the remaining numbers to balance equally across all three arms - test which number gives you the same sum on each arm.

Question T. Let us divide a 6 meter long cloth into pieces. If one meter is cut every time, how many times should we cut it?
Answer: We cut it 5 times. Each cut removes a one-meter piece. After the first cut, one meter is separate. After the second cut, another meter is separate. This continues until after five cuts, you have six pieces of one meter each. You need five cuts to divide a six-meter cloth into six one-meter pieces.
In simple words: To get 6 pieces from one long cloth, you need 5 cuts. Each cut separates one piece, but the last piece falls off without needing a cut.

Exam Tip: Remember: the number of cuts is always one less than the number of pieces you want - six pieces need only five cuts.

Question U. I think of a number and double it. If my answer is 18, then what was the number?
Answer: 18 is double of 9 so the number is 9.
In simple words: If you double a number and get 18, the starting number must be 9 because 9 times 2 equals 18.

Exam Tip: To find the original number when you know the doubled result, divide the result by 2.

Question V. Press 10 keys on a calculator to make 28.
Answer: Press the keys in this order: 5 × 4 = + 9 = - 1 = to get 28. First, 5 times 4 equals 20. Then add 9 to get 29. Finally, subtract 1 to reach 28. This uses exactly 10 keys on the calculator.
In simple words: Type 5, ×, 4, =, +, 9, =, -, 1, = on the calculator buttons in order to make 28. That is 10 button presses.

Exam Tip: Count each button you press - operation symbols (+, -, ×, ÷) count as keys, and the equals button (=) also counts toward your total of 10.

Question B. Complete the pattern.
Answer: The pattern shows two addition statements. The first line reads 2 + (blank) = 4, which means the missing number is 2. The second line reads 1 + 3 = (blank), so the missing number is 4.
In simple words: Find what number goes in each box. In the first line, what plus 2 makes 4? It's 2. In the second line, what is 1 plus 3? It's 4.

Exam Tip: Always work out the addition step by step. Double-check your answer by adding the numbers back together to make sure you get the result shown.

Question A. Draw lines to connect each pair of similar shapes together. The lines must not cross or touch each other and do not use diagonal lines.
Answer: Look at the grid and find the matching shapes. Connect the star to the star, the rectangle to the rectangle, the circle to the circle, and the triangle to the triangle. Use only straight lines that go up, down, left, or right - never go diagonally. Make sure your lines do not cross each other.
In simple words: Find two of the same shape and join them with a line. Your line can only go straight, not at an angle. Lines must not cross.

Exam Tip: Carefully check the shapes before drawing. Plan your path so lines do not cross each other - work through one pair at a time.

Question C. Think and complete.
Answer: The first pattern shows a square turning into a circle. Following this logic, the second pattern shows a star turning into a circle with the same red color. The answer is option (c).
In simple words: Look at what happens in the first example. The square becomes a circle. Now do the same thing to the star - it also becomes a circle.

Exam Tip: Find the rule in the first example and apply it to the second one. Check that your answer follows the same pattern.

Question C. Think and complete.
Answer: The letter C stands for 5. The letter e stands for 9. The number 7 stands for 7 (which could be read upside down as L). These are mirror-image style puzzles where you must think about what the letters or numbers look like when flipped.
In simple words: When you look at some letters or numbers in a mirror, they look like other numbers. C looks like 5 when flipped. e looks like 9.

Exam Tip: Try writing each letter or number and then look at it in a mirror. This shows you what it might represent in the puzzle.

Question D. Find the number.
Think of a number
Double that number
Add eight
Minus half of that number
Minus the number you started with
Is the number 4?
Now play this maths trick with your friends.
Answer: Let's work through this with the number 10:
Think of a number: 10
Double that number: 10 × 2 = 20
Add eight: 20 + 8 = 28
Minus half of that number: 28 ÷ 2 = 14
Minus the number you started with: 14 - 10 = 4
Yes, the number is 4.
In simple words: No matter what number you pick at the start, when you follow these steps, you always get 4 at the end. This works every time because the steps are designed that way.

Exam Tip: Try this trick with different starting numbers to see that it always gives 4. This shows how maths can create patterns that never change.

Question E. Look at the picture. How many different ways can the ant return to its home (anthill)?
Answer: The picture shows a grid with a path from the anthill to where the ant is. By counting all the different routes without going backwards, there are 5 different ways the ant can travel home. The answer shows five separate paths, each drawn with a dashed line, showing each unique route the ant could take.
In simple words: Count how many different paths the ant can take from where it is to its home. You can only move forward or sideways, not backwards. There are 5 different routes.

Exam Tip: When counting paths, make sure you never go backwards. Work systematically by tracing each route carefully to avoid missing any or counting the same path twice.

Question F. Find the number names from 11 to 20.
Answer: The word search contains the number names hidden in a grid of letters. The numbers from 11 to 20 that are hidden are: eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen, and twenty. These words run in different directions across, down, and diagonally through the letter grid. The answer shows which words have been found by highlighting the letters that spell out each number name.
In simple words: Find and mark the ten number names in the word search grid. They can go across, down, or at an angle.

Exam Tip: Start by looking for the first letter of each number name, then trace along that direction. Be patient and check both across and downward directions for each word.

Question G. Identify the appropriate shadow image.
Answer: Look at the main figure on the left, which shows a round, spiky object with multiple legs sticking out. The matching shadow is the dark silhouette that has the exact same round shape and the same number of legs pointing outward. The correct shadow is option (c), which shows the complete round outline with all the leg spikes matching the original image.
In simple words: A shadow shows the outline of something. Match the shape on the left with its shadow. Pick the dark outline that looks exactly the same as the original.

Exam Tip: Check the overall shape first, then count the legs or points. The shadow must match both the shape and the number of details.

Question H. In how many different ways can the cat return to its house?
Answer: In 3 different ways the cat can return to its house. The picture shows three separate routes marked with arrows and numbers (1), (2), and (3). Each route represents one different path the cat can take from its starting position to get back to its home. The routes show varied directions and paths across the rectangular garden area.
In simple words: The cat can go home using 3 different routes. Each path is marked with a different number to show the choices.

Exam Tip: When you see a maze or path problem, trace each route carefully from start to finish. Count each complete path as one way, making sure you don't count the same route twice.

Question I. Try to make two squares by removing two matchsticks.
Answer: To make two squares by removing two matchsticks from four connected squares, remove the two sticks in the middle that connect the squares. This leaves you with two separate squares - one on the left and one on the right. The answer shows three different solutions, each displaying which sticks were removed and resulting in two individual squares.
In simple words: You have four small squares joined together. Remove two matchsticks to leave just two separate squares.

Exam Tip: Carefully study which sticks hold the squares together. Try removing sticks one at a time to see the change in the shape.

Question J. Who am I?
I am in a bicycle,
And in a car and a bus,
I make all vehicles run,
They can't move if I am flat.
What is my shape?
Answer: Circle
In simple words: This is something round that you find in bikes, cars, and buses. When it becomes flat, vehicles cannot drive.

Exam Tip: Read the clues carefully. The answer describes something that is circular in shape and is essential for vehicles to move.

Question K. Which balls will you select to make a total of 30?
Answer: Select the balls numbered 11, 4, and 15 to make a total of 30. When you add these three numbers together: 11 + 4 + 15 = 30. The answer shows these three selected balls highlighted or marked in the answer grid.
In simple words: Pick three numbers from the list that add up to exactly 30. Check: 11 + 4 + 15 equals 30.

Exam Tip: Add the numbers together carefully to verify your total. Try different combinations if your first choice doesn't add up to 30.

Question L. Make two different two-digit numbers by using only one digit.
Answer: The two-digit numbers that use only one digit are: 11, 22, 33, 44, 55, 66, 77, 88, and 99. These numbers are formed by repeating the same digit twice. For example, 11 uses the digit 1 twice, 22 uses the digit 2 twice, and so on.
In simple words: Write a number twice to make a new two-digit number. For example, write 1 twice to get 11, or write 2 twice to get 22.

Exam Tip: Remember that a two-digit number has exactly two places. Use the same digit in both places to follow the rule of using "only one digit".

Question M. Draw a path so that hungry giraffe can reach the tree.
Answer: The maze shows a path marked with a dashed red line starting from where the giraffe is positioned and ending at the tree. The path winds through the maze passages, avoiding dead ends, until it reaches the green tree at the bottom right of the puzzle. Follow the dashed line to see the correct route from start to finish.
In simple words: Find a path through the maze that starts where the giraffe is and ends at the tree. Don't go up dead ends - keep going until you reach the tree.

Exam Tip: When solving mazes, try not to make random turns. Follow one direction until you reach a dead end, then backtrack and try another path.

Question N. Look at the above picture and write the answers.
(i) Name the animal whom giraffe met first on the path?
(ii) Name the animal whom giraffe met in the last?
(iii) Have you ever lost your way to home?
(iv) What do you do to remember your way to home?
Answer:
(i) Name the animal whom giraffe met first on the path?
Cat
(ii) Name the animal whom giraffe met in the last?
Bird
(iii) Have you ever lost your way to home?
Never
(iv) What do you do to remember your way to home?
I remember the landmarks.
In simple words: These questions are based on the picture story. The first animal you see is the cat. The last animal is the bird. Landmarks like buildings or trees help you find your way home.

Exam Tip: Look carefully at the picture in order to answer questions (i) and (ii). For questions (iii) and (iv), give your own honest answers based on your experience.

Question O. How many rectangles can be made after joining the dots given below?
Answer: 9 rectangles can be made. The grid of nine dots (arranged in three rows and three columns) allows you to form nine different rectangles by joining different combinations of dots. The answer shows all nine possible rectangles highlighted in orange lines on the dot grid, demonstrating each unique rectangle that can be created.
In simple words: A rectangle has four corners. Use the dots to make different rectangles. Remember that a square is also a type of rectangle.

Exam Tip: Organize your count by size. Find all small rectangles first, then look for larger ones. A square counts as a rectangle, so include those in your count.

Question P. Complete these by using addition or subtraction of numbers.
Answer: For the first hexagon with center value 9: 18 - 9 = 9 and 10 - 1 = 9 (all outer values combine with addition or subtraction to equal 9).
For the second hexagon with center value 13: 11 + 2 = 13 and 16 - 3 = 13 (all outer values work the same way).
For the third hexagon with center value 19: 25 - 6 = 19 and 16 + 3 = 19 (same pattern holds).
In simple words: Each number around the outside must combine with another number to make the number in the middle. You can add or subtract to get the center number.

Exam Tip: Find the pattern by checking two pairs first. Once you see whether addition or subtraction works, fill in all the remaining boxes using that same rule.

Question Q. A shepherd has 4 sheep and 4 dogs. Divide the garden into 4 areas, such that each portion or area contains one tree, one sheep and one dog.
Answer: The garden is divided into four sections using curved or straight dividing lines. Each section contains exactly one tree, one sheep, and one dog. The answer shows the original garden layout with the four trees, four sheep, and four dogs arranged so that when divided properly into four sections, each section has exactly one of each animal and one tree.
In simple words: You need to draw lines in the garden to make 4 equal spaces. Each space must have 1 tree, 1 sheep, and 1 dog inside it.

Exam Tip: Count carefully before dividing. Make sure each of your four sections has exactly one tree, one sheep, and one dog before finalizing your answer.

Question R. Who am I? (A mirror can help you)
(i) When you look at this in a mirror, it becomes 54.
(ii) When you look at this in a mirror, it becomes 83.
(iii) When you look at this in a mirror, it becomes 69.
(iv) When you look at this in a mirror, it becomes 71.
Answer:
(i) 45
(ii) 38
(iii) 69
(iv) 17
In simple words: Look at the numbers and write them backwards or in reverse. When you flip them, they look like different numbers. Some numbers look the same when flipped (like 6 and 9), but others change completely.

Exam Tip: Try holding each number up to a mirror or write it backwards to see what it becomes. This helps you understand how numbers look when reversed.

Question S. How will you arrange the numbers 1 to 7 so that the three arms have the same total?
Answer: Arrange the numbers so that the center circle contains 7, and the three arms each have numbers that add up to 12. One arrangement is: Place 7 in the center, then arrange the remaining numbers (1, 2, 3, 4, 5, 6) around it so that each of the three arms totals the same sum. The answer shows one such valid arrangement where each arm sums to 12.
In simple words: Put number 7 in the middle circle. Then arrange numbers 1 through 6 on the three arms so that each arm adds up to the same total.

Exam Tip: Start by placing the largest number in the center. Then work out what each arm should total by adding all numbers and dividing by 3.

Question T. Let us divide a 6 meter long cloth into pieces. If one meter is cut every time, how many times should we cut it?
Answer: We cut it in 5 times. When you cut a 6-meter cloth into 1-meter pieces, you need to make 5 cuts. The answer shows the cloth being cut five times with markers for the 1st time, 2nd time, 3rd time, 4th time, and 5th time, resulting in six separate 1-meter pieces.
In simple words: If you cut once, you get 2 pieces. If you cut twice, you get 3 pieces. To get 6 pieces from one long cloth, you need to cut it 5 times. Each cut makes one more piece.

Exam Tip: Remember that the number of cuts is always one less than the number of pieces you want. If you want 6 pieces, you need 5 cuts.

Question U. I think of a number and double it. If my answer is 18, then what was the number?
Answer: 18 is double of 9 so the number is 9.
In simple words: If doubling a number gives you 18, then that number must be half of 18, which is 9.

Exam Tip: When a problem says "double," use division to find the original number. Divide the answer by 2 to work backwards.

Question V. Press 10 keys on a calculator to make 28.
Answer: Press the keys in this order: 5 × 4 = + 9 = - 1 = to get 28. First, calculate 5 × 4, which gives 20. Then add 9 to get 29. Finally, subtract 1 to get 28.
In simple words: Follow this step by step: multiply 5 times 4 to get 20. Then add 9 to make 29. Then take away 1 to get 28.

Exam Tip: Work through calculator problems one step at a time. Always press = after each operation to see your result before continuing to the next operation.