Let's denote the five numbers as A, B, C, D, and E in descending order.
1. All the numbers are odd.
This means that all the numbers are of the form 2n + 1.
2. All the numbers have 2 digits.
Since the numbers have two digits, they range from 10 to 99.
3. The numbers add up to 97.
A + B + C + D + E = 97
4. The largest number is 25.
This implies that A = 25.
5. The second largest number is 4 more than the 3rd largest number.
B = C + 4
Now, let's substitute these values into the sum equation:
25 + B + C + D + E = 97
Substitute B with (C + 4):
25 + (C + 4) + C + D + E = 97
Combine like terms:
2C + D + E = 68
Considering the odd 2-digit numbers, let's try possible values for C, D, and E:
- C = 21, D = 23, E = 24 (21 + 23 + 24 = 68)
- A = 25, B = 25, C = 21, D = 23, E = 3 (25 + 25 + 21 + 23 + 3 = 97)
Therefore, the magic numbers are 25, 25, 21, 23, and 3.
