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Synthesize number puzzles, algorithmic traces, and mental logic from across the chapter.
Review the core skills covered in this chapter.
Progressive questions across chapter topics.
What is the 4-digit Kaprekar constant that you will eventually reach by repeatedly subtracting the smallest number formed by a set of 4 digits from the largest number formed by those same digits?
Find the sum and difference of largest and smallest palindromes.
Find the sum and difference of the smallest and largest 5-digit palindromes.
A palindrome reads the same forward and backward.
For example: 12321 is a palindrome because it reads the same both ways.
Recall the rule for a palindrome number.
Start with the smallest 5-digit number and adjust it so it reads the same forward and backward.
Think of the largest 5-digit number that reads the same forward and backward.
Add the smallest and largest 5-digit palindromes.
Subtract the smaller palindrome from the larger palindrome.
State both the sum and the difference clearly.
Manipulate a grid to maximize supercells.
Identify which two digits to swap in one of the numbers to create exactly 4 supercells in the grid.
| 16,200 | 39,344 | 29,765 | | 23,609 | 62,871 | 45,306 | | 19,381 | 50,319 | 38,408 |
A supercell is a cell containing a number greater than all of its immediate horizontal and vertical neighbours.
Only horizontal and vertical neighbours count. Diagonal neighbours do not count.
Check each cell against its immediate horizontal and vertical neighbours.
Look for a number that is close to becoming bigger than its neighbours after swapping two digits.
Choose two digits in that number and swap their positions.
Write the new number after exchanging the two digits.
List the cells that are now greater than all their immediate horizontal and vertical neighbours.
State the original number, the swapped digits, and confirm that the grid has exactly 4 supercells.