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

  • Thread starter Thread starter bracey
  • Start date Start date
  • Tags Tags
    Fun
AI Thread Summary
The discussion revolves around finding a unique 5-digit number that meets specific criteria, including having no identical digits, two perfect square digits, two prime digits, and one digit that is neither. The conditions also specify relationships between the digits, such as the second digit being six less than the fourth and the last digit being half of the third. Initial attempts to solve the puzzle included various combinations, but they failed to meet all conditions. Ultimately, the number 73894 is proposed as the correct solution. The conversation highlights the challenge of satisfying all mathematical constraints while ensuring digit uniqueness.
bracey
Messages
6
Reaction score
0
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?
 
Mathematics news on Phys.org


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
 
none of those digits satisifies 'neither prime nor square'
 
Originally posted by matt grime
none of those digits satisifies 'neither prime nor square'
oh, you're right :(
 
I think the answer is 73894.
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.
Back
Top