A Python-free math quest on patterns, puzzles and Kaprekar tricks.
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Q1: What is the Kaprekar constant?
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Q2: What is the biggest number in Table 2 (from the solutions) that has five digits?
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Q3: How many rounds does starting number 5683 take to reach Kaprekar constant 6174?
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Q4: The smallest 5-digit palindrome is?
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Q5: Which time is a palindromic time on a 12-hour clock?
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Q6: What is the next palindromic time after 10:01?
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Q7: In the 5-digit palindrome puzzle, which is closest to 50,000 with repeating digits?
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Q8: How many digits are there in 1–9 (one-digit numbers)?
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Q9: In Collatz sequences, starting from 12, what is the next term?
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Q10: If a cell is the Kaprekar constant example, what is the base rule?
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Q11: Which of the following is a 12-hour palindromic time?
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Q12: The sum of smallest and largest 5-digit palindrome is?
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Q13: Which pattern best completes the Collatz sequence visualization starting with an even number?
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Q14: The smallest even number in the 4x4 Kaprekar table example is?
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Q15: What is the Kaprekar constant for a 3-digit sequence (if it exists in the puzzle)?
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Q16: Which of these dates forms a X-shaped date palindrome (past example)?
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Q17: The biggest 4-digit number in a particular supercell puzzle example is?
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Q18: In number play, which operation can yield a 6-digit sum from two 4-digit numbers?
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Q19: In the ‘Patterns on the Number Line’ activity, which set of numbers sits left of 4000?
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Q20: The Collatz sequence example starting with 21 ends with which number?
Feedback
6174 is reached when you repeat the Kaprekar routine on 4-digit numbers with at least two different digits.
In the provided solution Table 2, the largest 5-digit number shown is 96,310.
According to the example, 5683 requires 8 rounds to reach 6174.
The smallest 5-digit palindrome using digits is 10001.
Palindromic times read the same forward and backward (e.g., 4:44, 10:01, 12:21).
The next palindromic time after 10:01 is 11:11.
Among 5-digit palindromes with all digits odd and near 50k, 51,111 is closest.
There are exactly 9 one-digit numbers, i.e., 1-digit numbers.
If even, you divide by 2; 12 → 6.
Kaprekar process uses max-min from digits to form next term.
Palindromic times read the same forwards and backwards; 4:44 is one example.
Smallest 5-digit palindrome is 10001 and largest is 99999; sum 110000.
Collatz rule: if even, halve; if odd, 3n+1.
From the solved table, smallest even is 10,396.
For 3-digit Kaprekar, the constant is not established/proven in the chapter.
Dates like 20/12/2012 read similarly left-to-right and right-to-left.
In the example, 9435 is a larger candidate in the grid.
The chapter discusses possible cases; some 4+4 can yield 6-digit sums.
The line example places numbers across ranges; 2180 and 2754 appear left of 4000.
All Collatz sequences in the example terminate at 1.
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