To find the mystery number, let’s start by analyzing each clue.
Clue #1 tells us that the mystery number is a two-digit number (since it's less than 100 but greater than 10).
Clue #2 says that you use a total of 12 base ten blocks to show this number. This means that the sum of the tens and ones places must add up to 12. Importantly, the clue also specifies that the number of tens blocks is less than the number of ones blocks. This means that the digit in the tens place must be less than the digit in the ones place.
Clue #3 informs us that one of the digits in the number is 8.
To solve for this mystery number, let’s enumerate all possibilities based on these clues. Since we need to make 12 with two digits and the tens digit must be smaller than the ones digit, we can start by pairing numbers that sum to 12:
- 1 and 11 (not possible since 11 is not a single digit)
- 2 and 10 (not possible since 10 is not a single digit)
- 3 and 9
- 4 and 8
- 5 and 7
- 6 and 6 (not possible since the tens digit can't be equal to the ones digit)
Out of these possibilities, we can immediately rule out pairs where the first number isn't less than the second number, as well as those that aren’t comprised of single-digit numbers.
Now we have the pairs:
- 3 and 9
- 4 and 8
- 5 and 7
From Clue #3, we know that one of the digits must be 8. So the only pair from our list that includes 8 is 4 and 8.
Knowing now that we have a 4 and an 8, and that the tens digit must be less than the ones digit, the only number we could form is 48.
So, the mystery number that satisfies all three clues is 48.
