Level B

1. Pick any 2-digit number where not all the digits are equal.

2. Order the digits from highest to lowest to create the largest number.

3. Order the digits from lowest to highest to create the smallest number.

4. Find the positive difference between the two numbers.

5. Investigate different solutions you find.

6. Are there patterns? If so, what patterns did you find?

The number has 2 digits - let's call them x and y. The positive difference between the two combinations (lowest-highest and highest-lowest) is always equal to the positive difference of x and y, multiplied by 9.
For example:
76 and 67: 76 - 67 = 9 and ((7-6) 9) = 1 9 = 9 73 and 37: 73 - 37 = 36 and ((7-3) 9) = 4 9 = 36

Answered by DavidOrrell | 2024-06-10

To explore the digits of a 2-digit number, first arrange them from highest to lowest and then from lowest to highest. The positive difference between these two new numbers can reveal interesting patterns, often reflecting multiples of 9 based on how different the digits are. Each combination of digits can lead to similar conclusions about their differences playing consistently into the base of 9, making this a fun exploration into number properties.
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Answered by DavidOrrell | 2024-12-26