(a) Only Sometimes True: A person says ‘0’ when they see no one taller than themselves. The tallest person will always say ‘0’, but a shorter person can also say ‘0’ if they are at the front or in a position where no one taller is ahead of them. Thus, the given statement is only sometimes true. (b) Always True: If a person is the tallest, then no one is taller than them, so they will always say ‘0’. So, the given statement is always true. (c) Always True: Each person is assigned a number that represents how many taller people are ahead of them. Since there is no one ahead of the first person, their number will always be ‘0’. Hence, the given statement is always true. (d) Only Sometimes True: The statement is only sometimes true. A person standing in between can still be assigned ‘0’ if there are no taller people ahead of them. (e) Only Sometimes True: The statement is only sometimes true. A person who calls out the largest number has many taller people in front but may not be the shortest overall. For example, if the shortest person is standing at the front, they will call out ‘0’. Meanwhile, the second shortest person could be at the back and might call out the largest number. (f) If there are 8 people, then the shortest person will see 7 taller people. So the maximum number someone can say is 7. 6.2 Picking Parity NCERT In-Text Questions (Pages 129-131) Kishor has some number cards and is working on a puzzle: There are 5 boxes, and each box should contain exactly 1 number card. The numbers in the boxes should sum to 30. Can you help him fid a way to do it? Can you figure out which 5 cards add to 30? Is it possible? Solution: No, it is not possible, as the sum of 5 odd numbers is always odd and 30 is an even number. Explore what happens to the sum of (a) 4 odd numbers, (b) 5 odd numbers, and (c) 6 odd numbers. Solution: Based on the given examples for number cards 1, 3, 5, 7, 9, 11, 13. (a) Sum of 4 odd numbers = 1 + 3 + 5 + 7 = 16 (even), can be arranged in pairs. (b) Sum of 5 odd numbers = 1 + 3 + 5 + 7 + 9 = 25 (odd), cannot be arranged in pairs. (c) Sum of 6 odd numbers = 1 + 3 + 5 + 7 + 9 + 11 = 36 (even), can be arranged in pairs. Figure it Out (Page 131)