Question

A natural number ends in 2. If we move this digit 2 to the beginning of the number, then the number will be doubled. Find the smallest number with this property.

Answer 1

@Numb3r1

Answer 2

ab...2=2ab.../2
more specifically, whatever number ab... is (multiple digits, clearly, as 2d cannot equal d2*2 because that would be (2d)4, but 42 is not twice 24 or vice versa)
ab... times ten plus two equals 2*10^(?) plus ab....

Answer 3

ok

Answer 4

That means 2*10^(?)=9(ab...) plus 2. ab... must end in a 2, because 9*ab.... ends in an 8 to make 9*ab...+2 end in a zero.

Answer 5

ok

Answer 6

Wait, that has so many issues... ignore it.

Answer 7

ok

Answer 8

Here's a fixed version:

Answer 9

ok

Answer 10

That means 2*10^(?)+ab...=20(ab...) plus 2. The twenty accounts for the doubling of the original number.

Answer 11

Therefore, 2*10^(?)=19(ab...) plus 2. 2*10^(?)-2 looks like 19....98. Divide by 19 and we have 1...?

Answer 12

Nope, that makes no sense.

Answer 13

ab2=2ab/2... let's see... ab must start in a 1, so I was right anyway.

Answer 14

Unless we carry... that's it!

Answer 15

ok

Answer 16

2ab2=ab22*2... nope. I should just go to sleep. Good luck!

Answer 17

ok

Answer 18

Thank you sir

Answer 19

105263157894736842