Find a 5-Digit Number with Unique Prime & Square Digits

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The first digit (7) is three greater than the last digit (4), the second digit (3) is six less than the fourth digit (9), and the last digit (4) is half of the third digit (8). The digits 3, 7, and 8 are all prime numbers, while the digits 3 and 4 are perfect squares. Therefore, this number satisfies all the given conditions. In summary, the conversation was about finding a 5 digit number that met certain criteria, such as having no identical digits, having two perfect squares, two prime digits, and one digit that was neither prime nor a perfect square. After some trial and error, the number 73894 was determined to be the
  • #1
bracey
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Just abit of fun!

Find a 5 digit number that:
· Has no two identical digits.
· Has two digits that are perfect squares.
· Has two digits that are prime.
· Has one digit that is neither prime, or a perfect square.
· That has the second digit six less than the fourth digit.
· That has the last digit half of the third digit.
· That has the first digit three greater than the last digit.
What's the number?
 
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  • #2


Originally posted by bracey
Find a 5 digit number that:
· Has no two identical digits.
· Has two digits that are perfect squares.
· Has two digits that are prime.
· Has one digit that is neither prime, or a perfect square.
· That has the second digit six less than the fourth digit.
· That has the last digit half of the third digit.
· That has the first digit three greater than the last digit.
What's the number?
ABCDE
A49DE
A3492
53492

am I right? that is how my process went
 
  • #3
none of those digits satisifies 'neither prime nor square'
 
  • #4
Originally posted by matt grime
none of those digits satisifies 'neither prime nor square'
oh, you're right :(
 
  • #5
I think the answer is 73894.
 

1. What is a 5-digit number with unique prime and square digits?

A 5-digit number with unique prime and square digits is a number that contains 5 digits, each of which is a prime number or a perfect square, and no digit is repeated.

2. How many 5-digit numbers with unique prime and square digits are there?

There are 9,720 5-digit numbers with unique prime and square digits.

3. Can 0 be included in a 5-digit number with unique prime and square digits?

No, 0 cannot be included in a 5-digit number with unique prime and square digits as it is not a prime number or a perfect square.

4. What is the smallest 5-digit number with unique prime and square digits?

The smallest 5-digit number with unique prime and square digits is 12,345.

5. How can I check if a 5-digit number has unique prime and square digits?

To check if a 5-digit number has unique prime and square digits, you can first check if each digit is a prime number or a perfect square. Then, you can compare each digit with the rest of the digits to ensure that there are no duplicates.

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