It’s a simple question, really, but one that can spark a bit of fun and a good dose of logical thinking: how many unique two-digit numbers can you create using the digits 8, 2, and 5, without repeating any digit within a number? And once you've made them, which one is the biggest, and which is the smallest?
Let's dive in. We've got three distinct digits to play with: 8, 2, and 5. The goal is to form two-digit numbers. This means we need a digit for the tens place and a different digit for the units place.
Think of it like picking two distinct items from a set of three. For the tens place, we have three choices: 8, 2, or 5. Once we've picked a digit for the tens place, we only have two digits left for the units place.
Let's lay it out systematically, just like you might do on a small whiteboard:
- If 8 is in the tens place: We can pair it with 2 (giving us 82) or with 5 (giving us 85).
- If 2 is in the tens place: We can pair it with 8 (giving us 28) or with 5 (giving us 25).
- If 5 is in the tens place: We can pair it with 8 (giving us 58) or with 2 (giving us 52).
So, by listing them out, we find we can create a total of six different two-digit numbers: 82, 85, 28, 25, 58, and 52. It's neat how a small set of numbers can branch out into so many combinations!
Now, for the second part of the puzzle: finding the largest and smallest among these. Looking at our list – 82, 85, 28, 25, 58, 52 – it’s pretty straightforward to spot the extremes. The numbers starting with 8 are clearly going to be larger than those starting with 2 or 5. Between 82 and 85, 85 is the bigger one. And when we look at the numbers starting with 2 or 5, the smallest ones will be those starting with the smallest digit, which is 2. Between 28 and 25, 25 is the smallest.
Therefore, the largest number we can form is 85, and the smallest is 25. It’s a lovely little exercise in place value and logical deduction, proving that even with just a few digits, there’s a whole world of numbers to explore.
