Question 1201159: PUZZLE CORNER
Enter PIN code
ENTER PIN CODE
O
Albert changed his mobile phone PIN code from 0000 but he has now forgotten it. He remembers that if you multiply it by 4, the answer is the PIN code in reverse.
Can you help him?
Answer by greenestamps(13198)   (Show Source):
You can put this solution on YOUR website!
his PIN code is ABCD; and multiplied by 4 it is DCBA.
ABCD
x 4
----
DCBA
4 is an even digit; an even digit times any digit yields an even last digit, so A is even.
4 times ABCD is still a 4-digit number; then, since A must be even, A can only be 2.
2BCD
x 4
----
DCB2
The multiplication D times 4 yields final digit 2, so D can be only 3 or 8. But 4 times 2BCD yields first digit D, so D must be 8.
2BC8
x 4
----
8CB2
8CB2 is a multiple of 4, so the last 2 digits of 8CB2 must be a multiple of 4. That means B is odd.
But 4 times 2BC8 yields a 4-digit product, so B must be 1.
21C8
x 4
----
8C12
4 times the last 2 digits C8 yields last 2 digits 12 in the product; that means C can be only 2 or 7. But since 4 times 21C8 yields the product 8C12, C must be 7.
2178
x 4
----
8712
ANSWER: His PIN code is 2178
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