Question 3 of 16advanced✨ CreateLong Answer5 marks

Two friends decide who gets the last slice of a cake by flipping a coin five times. The first person to win three flips wins the cake. An input of 1 means player 1 wins a flip, and a 2 means player 2 wins a flip. Design an algorithm to determine who takes the cake?

Correct Answer

To solve this problem, we need to identify the input, process, and output. The input is the result of each coin flip (1 for Player 1 winning, 2 for Player 2 winning). The process involves counting the wins for each player and checking after each flip if either player has reached 3 wins. The output is the declaration of which player takes the cake.

The algorithm uses a repetition structure to flip the coin multiple times. We use counters to keep track of wins for both players. After each flip, we check if either player has won 3 flips, and if so, we declare them the winner immediately.

Pseudocode: SET count1 = 0, count2 = 0 SET flips = 0 WHILE flips < 5 AND count1 < 3 AND count2 < 3 INPUT result IF result == 1 THEN INCREMENT count1 ELSE INCREMENT count2 END IF INCREMENT flips END WHILE IF count1 >= 3 THEN PRINT "Player 1 takes the cake" ELSE IF count2 >= 3 THEN PRINT "Player 2 takes the cake" ELSE IF count1 > count2 THEN PRINT "Player 1 takes the cake" ELSE IF count2 > count1 THEN PRINT "Player 2 takes the cake" ELSE PRINT "It is a tie" END IF

The algorithm uses decision making with IF-ELSE statements to determine the winner based on the conditions specified. The WHILE loop ensures that the game stops as soon as one player reaches 3 wins, even before all 5 flips are completed.

Exercise: EXERCISE | Q: 2 | (Page 23)
For More Understanding

Explanation

This answer follows the NCERT textbook pattern of identifying input, process, and output as demonstrated in Example 4.7 (Dragons and Wizards card game). The pseudocode uses IF-ELSE for decision making and WHILE for repetition, which are key concepts from the chapter. The algorithm correctly handles the early termination condition when a player reaches 3 wins.

Solution Steps

  1. Step 1: Identify input (coin flip results: 1 or 2), process (count wins and check for winner), and output (winner declaration)

  2. Step 2: Initialize counters count1 and count2 to 0 for tracking wins

  3. Step 3: Use WHILE loop to continue until 5 flips done OR someone wins 3 flips

  4. Step 4: Inside loop, input result and INCREMENT respective counter using IF-ELSE

  5. Step 5: After loop, use nested IF-ELSE to check conditions and PRINT the winner

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