What is the five digit number ?

Question

Can you find a five digit number which has no zeros and no repeated digits, where:

The first digit is a prime number.
The second digit is the fifth digit minus the first digit.
The third digit is twice the first digit.
The fourth digit is the third digit plus three.
The fifth digit is the difference between the first digit and the fourth digit ?

Answer 1

The answer is 23475.

Let's look at how I got there:


The first digit is a prime number: 2,3,5,7

One is not a prime, so anything starting with 1 is not actually an option. There are two valid numbers, but one of them has repeating digits.

Good. That narrows it down a lot.

The third digit is twice the first digit: Following from the numbers possible for the first digit, it's 4,6,10,or 14. It obviously cannot be the last 2 since they are two digits. That means it is either 4 or 6, and the first digit is 2 or 3.

So far we have
2x4xx or
3x6xx

The fourth digit is the third digit plus 3. That's easy. We now have
2x47x or
3x69x

The fifth digit is the difference between the first digit and the fourth digit. 7-2=5 and 9-3=6 We now have

2x475 or
3x696

Wait! The second number has a repeated digit, 6. It thus cannot be the number.

Let's go on with option 1. The second digit is the fifth digit minus the first digit. 5-2=3

The number is 23475.


Hope this helps.

Answer 2

1st = a = Prime number
2nd = b = e - a
3rd = c = 2a
4th = d = c + 3
5th = e = a - d

a can be 2 or 3 (because of c; 2(5) and 2(7) are not one digit)
b can be (e - a)
c can be: 4 (if a = 2) or 6 (if a = 3)
d can be 7 (if c = 4) or 9 (if c = 6)
e can be: 2, 4, 6, 7 (if d is 9) or 2, 4, or 5 (if d is 7)

Trial and Error: We'll let a = 2
a = 2, b = 3, c = 4, d = 7, e = 5
Since all the digits fit the critera, I think we got it on our 1st guess:

Answer: 23,475
Check:
2 is prime
3 = (5) - (2)
4 = 2(2)
7 = (4) + (3)
5 = | (2) - (7) | --- | | denotes absolute value...

Answer 3

So... abcde, where a,b, d, c, e are all different.

(1) a is prime
(2) b=e-a
(3) c=2a
(4) d=c+3
(5) e=|a-d|

If a>d then from (5) we have e=a-d or e-a=-d and from (2) we have -d=b. Impossible if d and b are digits from 1 to 9. So we can rewrite (5) as
(5) e=d-a.

Now
b = e-a from (2)
b = d-a-a substituting (5) for e
b = d-2a
b = d-c substituting (3)
b = 3 substituting (4).

So (2) becomes e-a=3. The only possibilities for prime a are:
a=2, e=5
a=5, e=8

The second case yields d=13 from (5) so it won't work.

The first case gives us d=7 from (5), and c=4 from (3). So the answer is 23475.

Answer 4

23475.

(let us take smallest prime nomber as 2.
The third digit is twice the first digit.=2*2=4
The fourth digit is the third digit plus three=4+3=7.
The fifth digit is the difference between the first digit and the fourth digit
=7-2
=5
The second digit is the fifth digit minus the first digit.
=5-2
=3

Answer 5

All are divisible by 1. Exactly half are divisible by 2. 10000 is 1 mod 3. 99999 is 0 mod 3, so exactly 1/3 are divisible by 3. 10000 is 0 mod 4. 99999 is 3 mod 4, so exactly 1/4 are divisible by 4. 10000 is 0 mod 5. 99999 is 4 mod 5, so exactly 1/5 are divisible by 5. A number that is divisible by 1, 2, 3, 4, and 5 is divisible by 60. 10000 is 40 mod 60. 99999 is 39 mod 60. So exactly 1/60 are divisible by all of 1, 2, 3, 4, and 5.

Answer 6

first - 2,3,5,7

third digit <10 => first digit = 2,3
if first = 2 then third = 4 and fourth = 7 and fiftth= 5
and second = 3 ... qed

23475 fits

Answer 7

23,475

Set up a grid and gradually tick or cross what each number can or can't be.

for example, the third digit must be even - cross out all the odd numbers.

The third digit can't be 7,8 or 9 either because if you add three to either of those it is more than nine and the fourth digit can't be ten or more.

Keep going and you'll be able to figure them out

Answer 8

23475 is the right answer, 1 is it not a prime number, since it only has one factor, where a prime number is supposed to have exactly 2.

Answer 9

23475
I wont go into how I got it as Aegor has done that beautifully already...;

Answer 10

23475