A three digit (non leading zero) positive integer N is such that by adding 3 to N and dividing the result by 4 we obtain the reversal of N.
Determine the value of N.
Note: Computer program solutions are welcome but an analytical solution is preferred.
Just as this process reverses 661 to 166,
it works for any concatenation of 6s follow by a single 1.
Adding the 3 makes it a little less than (2/3)*10^k, the error is 8/3 of a unit.
Then dividing by 4 makes it it a little less than (1/6)*10^k, the error is 2/3 of a unit.
The first error is 4 times the second error.
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Posted by Larry
on 2023-05-13 18:32:23 |
a slight generalization
