Question 978869: Timothy changed his mobile phone pin code from 0000 but he has now forgotten it.He remembers thar if you multiply it by 4,the answer is the pin code is reverse.Can you help Timothy retrieve it?
Found 3 solutions by CubeyThePenguin, ikleyn, greenestamps:
Answer by CubeyThePenguin(3113)   (Show Source):
Answer by ikleyn(52898)  (Show Source):
You can put this solution on YOUR website! .
The answer by @CubeyThePenguin is INCORRECT.
The correct answer is 2178.
For detailed solution, see this link
https://www.quora.com/A-4-digit-number-multiplied-by-4-gives-same-number-in-reverse-order-What-is-the-four-digit-number-and-how-do-I-prove-it
Answer by greenestamps(13214)  (Show Source):
You can put this solution on YOUR website!
New tutor @CubeyThePenguin is supplying a lot of useful responses; but far too often he isn't answering the question that is asked; and -- even worse -- he is often giving answers without showing HOW to get the answers, which is of no benefit at all to the student.
And in this case he has given a wrong answer, also without showing any work....
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Here is the problem....
ABCD
* 4
----
DCBA
(1) A must be either 1 or 2; otherwise the product would not be 4 digits.
(2) Since the PIN multiplied by 4 has last digit A, A must be even.
(3) (1) and (2) tell us A is 2.
2BCD
* 4
----
DCB2
(4) D multiplied by 4 gives last digit 2, so D must be either 3 or 8.
(5) D is the leading digit of the product of 2BCD times 4, so D must be 8.
2BC8
* 4
----
8CB2
(6) 4 times C8 gives B2; 4 times C is even, and since 8 times 4 is 32, B must be odd. So B is 1, 3, 5, 7, or 9.
(7) 4 times 2BC8 gives a product with leading digit 8.
(8) (6) and (7) tell us B must be 1.
21C8
* 4
----
8C12
(9) 21?? times 4 gives 8C??, so C must be at least 4.
(10) C8 times 4 gives final two digits 12; that means C is either 2 or 7.
(11) (9) and (10) tell us that C is 7.
2178
* 4
----
8712
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