This is a riddle, and I'm supposed to find a 5-digit number from it.....
My thousand's digit is the first that is perfect,
but if you're not happy with that,
it's also the product of the first two primes.
My units digit is the odd of those two primes,
and if you look at it and my tens,
you'll find a number divisble by three, but not by the square of that my friends.
Now let's look at my hundreds and thousands
If you examine those two as they're paired, you'll find they form a number divisible by an even prime that's been squared. (4)
Now let's look at my body in whole. Five different digits you see, in order (or not) you'll find that they are divisible by nine,
Can you find the mystery number?
I think I have the thousands and hundreds digits...
Hundreds: 3
Thousands: 6
To solve this riddle and find the 5-digit number, let's break down the clues one by one.
1. The thousand's digit is the first that is perfect and is also the product of the first two primes.
The first perfect number is 6, so the thousand's digit is 6. The first two primes are 2 and 3, so multiplying them gives 6.
2. The unit's digit is the odd of those two primes.
The two primes are 2 and 3, and the odd one is 3. Therefore, the unit's digit is 3.
3. The number formed by the unit's and tens' digits is divisible by 3 but not by the square of that.
Since the unit's digit is 3, we need to find a tens' digit that, when combined with 3, forms a number divisible by 3 but not by 9. The only option is 6, as 36 is divisible by 3 but not by 9.
4. The hundreds and thousands digits form a number divisible by the square of an even prime (4).
We already know the thousands digit is 6. The only digit left is 4, and since it is an even number, it fits the clue. So the hundreds digit is 4.
5. The five digits are all divisible by 9.
Since we know the digits so far are 6, 4, 3, and we need two more digits that are divisible by 9, we can try different combinations to see which ones work:
- 64339 → 6 + 4 + 3 + 3 + 9 = 25 (not divisible by 9)
- 63439 → 6 + 3 + 4 + 3 + 9 = 25 (not divisible by 9)
- 46339 → 4 + 6 + 3 + 3 + 9 = 25 (not divisible by 9)
- 43639 → 4 + 3 + 6 + 3 + 9 = 25 (not divisible by 9)
- 34963 → 3 + 4 + 9 + 6 + 3 = 25 (not divisible by 9)
- 39463 → 3 + 9 + 4 + 6 + 3 = 25 (not divisible by 9)
- 43963 → 4 + 3 + 9 + 6 + 3 = 25 (not divisible by 9)
- 49363 → 4 + 9 + 3 + 6 + 3 = 25 (not divisible by 9)
- 93463 → 9 + 3 + 4 + 6 + 3 = 25 (not divisible by 9)
- 94363 → 9 + 4 + 3 + 6 + 3 = 25 (not divisible by 9)
None of the combinations satisfy the divisibility by 9 requirement. Therefore, the given clues do not lead to a valid 5-digit number.