Could you help me with a mystery number problem?

Question

I have one problems, it's a number problem where you have to find the mystery number. I'm stuck, and have done some work, but don't know how to continue. Could someone please explain to me how to complete this problem (and what a placeholder is?)

a. I am a four-digit number.
b. I am a multiple of 25.
c. I have an odd number of factors.
d. None of my digits are the same.
e. None of my digits is a square number

I got that the number ends in 25 and the other two digits have to be some form of 3,6,7 or 8. ( In pairs)

PLEASE HELP!!!!!!!!!!
And thanks in advance for the help.

Good point, never mind about what I got. I'm wrong!!!!!

Answer 1

Four-digit multiples of 25 can end in 00, 25, 50, or 75. But 00 is out because none of the digits are the same, so your number must end in 25, 50, or 75.

"None of my digits is a square number" means that 4 or 9 cannot appear in the number.

"Has an odd number of factors" means that it needs to be a perfect square.

55^2 = 3025 fits the bill

(found by starting with 32*32 in calc and looking for the first one that was divisible by 25 and had no repeating digits and no 4 or 9)

The prime factorization is 5*5*11*11 so the factors are

1, 5, 25, 55, 275, 605, and 3025 = 7 factors

Answer 2

If it has an odd number of factors, that means it must be a perfect square.

If none of the digits is a perfect square, none of the digits can be 0, 1, 4, or 9.

A multiple of 25 must end in 00, 25, 50, or 75. But if it can not end in 0, it must end in 5.

Let's look for 4 digit squares. since it is a multiple of 25, it's square must be a multiple of 5. Since the number must be odd, it's square must be odd.

35^2=1225, but that doesn't work, since no two digits can be the same. 45*45=2025, but that does not work since it has a 0 in it. 55*55=3025, ditto. 65*65=4225, ditto. 75*75=5625 which has two digits the same.

OK, I can't get anything to work. I'm stumped. AARRGGHHH

I looked at the above answers. Several people say 3025. but that doesn't work, since 0 is a square number !!!!!!!!!!!!!!

Answer 3

from (a) your number is _ _ _ _
from (b) your number is either
_ _ 25
_ _ 50
_ _ 75
_ _ 00, because 25 is divisible by only those choices
from (c) you go back to that later
from (d) you can rule out _ _ 00
and from (e) you can rule out _ _ 50 leaving you with
_ _ 25 and _ _ 75, now go back to (c), you have an odd number of factors meaning that the number must been a squared number, b/c you always get two factors, but for squared numbers you get yourself and don't list yourself twice,
For example 6 has factors 1,6 and 2,3 but
4 has factors 1,4 and 2,2 or 1,2,4 cause you don't repeat the two

b/c the number is squared your number is either divisible by 25 or by 25^2 = 625, guess and check the number by multiplying 25 by an odd squared number, b/c an even squared number would make the four digit number even but it ends in 5

from my guessing and checking i multiply 25 by 19^2 to get: 9025, but 9 is a squared number

hope my explanation helps you get the answer

ps. the number that works is 25 * 11^2 = 3025

Answer 4

this is virtually unsolvable for a kid doing homework. Now, if you are a PHD math student...yeah, I can see this being a year long project.

1025
1750
1325..the list of choices is friggin endless. How am I supposed to sit down and figure out which 4 digit number only has 3 factors.

ALSO 2 is not a square..if you think it is, please tell me what number, multiplied by itself =2!!!!

Answer 5

the finest innovations-set to this undertaking in keeping with probability is to apply brute rigidity seek set of rules.. This application (in Java) tests all a threat solutions (00, 01, 02, ... ninety 8, ninety 9) the respond is 25! public type answer { public static void significant (String[] args) { for (int x=0 ; x<=9 ; x++) { for (int y=0 ; y<=9 ; y++) { if (Math.pow(10*x+y,2)==618+x+y) { device.out.println("effect: " + x + "" + y ) ; } } } device.out.println("----no longer something follows----") ; } }

Answer 6

Why can it not end in 50 or 75?