Number Play — Hard

Q1. Five children of different heights are arranged in a line so that the maximum possible number of children say '2'. What is that maximum, and what does the arrangement look like?

• A. 1, with all five tall children together
• B. 2, with the pattern shortest-tall-short-tall-shortest
• C. 3, with the tallest in the middle
• D. 5, when heights are equal

Q2. Assertion (A): For a group of 5 children of different heights, the sequence 1, 1, 1, 1, 1 is impossible. Reason (R): The tallest child in any line has no taller neighbour, so cannot say '1'.

• A. Both A and R are true, and R is the correct explanation of A.
• B. Both A and R are true, but R is NOT the correct explanation of A.
• C. A is true, R is false.
• D. A is false, R is true.

Q3. For a single row of n cells filled with distinct numbers, what is the maximum number of supercells possible? Choose the BEST statement.

• A. Always 1, the largest number
• B. Always n − 2, excluding the two ends
• C. n/2 for even n and (n−1)/2 for odd n
• D. n/2 for even n and (n+1)/2 for odd n

Q4. Table 2 must be filled with 5-digit numbers using only the digits 1, 0, 6, 3 and 9 (each digit used once per number) so that the green cells are exactly the supercells. What is the biggest number that appears in the completed table?

• A. 96,310
• B. 96,301
• C. 93,610
• D. 90,631

Q5. Among the whole numbers from 1 to 1000, how many times does the digit '7' appear in total?

• A. 100
• B. 200
• C. 271
• D. 300

Q6. Calculate digit sums of 3-digit numbers whose digits are three consecutive whole numbers (e.g., 123, 234, 345, …, 789). The sums are 6, 9, 12, 15, 18, 21, 24. What pattern do these sums show?

• A. They are all multiples of 2.
• B. They are all multiples of 3.
• C. They are all prime numbers.
• D. They are all multiples of 6.

Q7. Solve the palindrome puzzle. The mystery 5-digit number is a palindrome, is odd, its tens digit is double its units digit, and its hundreds digit is double its tens digit. What is the number?

• A. 12321
• B. 24642
• C. 36963
• D. 48984

Q8. What is the sum of the smallest and largest 5-digit palindromes?

• A. 1,09,999
• B. 1,09,901
• C. 1,10,099
• D. 1,10,000

Q9. How many rounds of the Kaprekar process does the starting number 5683 take to reach the Kaprekar constant 6174?

• A. 1 round
• B. 2 rounds
• C. 3 rounds
• D. 4 rounds

Q10. Consider the following statements about the Kaprekar process: I. The process needs a 4-digit starting number. II. The starting number must have at least two different digits. III. Numbers like 1111 or 2222 will also reach 6174. Which are correct?

• A. I and II only
• B. II and III only
• C. I and III only
• D. All three

Q11. On, the middle column has the numbers 25,000, 400, 13,000, 1,500 and 60,000 (each usable any number of times by addition). Which combination gives 3,400?

• A. 1,500 + 1,500 + 400
• B. 13,000 − 9,600
• C. 1,500 + 400 + 400 + 400 + 400 + 400
• D. 25,000 − 21,600

Q12. Consider the statement: 'A 4-digit number + a 2-digit number can give a 6-digit number.' Is this Always, Sometimes or Never true?

• A. Always true
• B. Sometimes true
• C. Never true
• D. True only when both numbers end in 9

Q13. Consider the statement: 'A 5-digit number minus a 5-digit number gives a 5-digit number.' Is this Always, Sometimes or Never true?

• A. Always true
• B. Never true
• C. Sometimes true
• D. True only when both have the same first digit

Q14. On, the (c) figure has a 4 × 8 = 32 block of 32s on top and a 4 × 4 block of 64s with a 4 × 1 column of 64s on the side (32 cells of 32 and 20 cells of 64). What is the total?

• A. 1024
• B. 2272
• C. 2280
• D. 2304

Q15. In Game #1 (first to reach 21 wins, each turn adds 1, 2 or 3), what sequence of 'target' numbers should the winning player aim to say so as to force a win?

• A. Multiples of 4 only — 4, 8, 12, 16, 20
• B. Odd numbers only — 1, 3, 5, …, 21
• C. There is no winning strategy; the game is luck
• D. 1, 5, 9, 13, 17, 21 — every fourth number starting from 1