Op 10-12-2020 om 10:45 schreef Dave Moore:
That integer can't end in a 1, so it has to be a multiple of 360 ( =5 * 72).
If we cut off the last digit, the question becomes "which multiple of 36
(360 without last zero) has only 1's and 0's?
Again, last digit can't be a 1, so we must look at multiples of 36 which
end in a zero. That means we have multiples of 180 (= 5*36).
And now again we drop a digit and the question becomes: "which multiple
of 18 has only 1's and 0's?
And again, last digit can't be a 1, so we must look at multiples of 18
which end in a zero. That means we have multiples of 90 (= 5*18).
And now again we drop a digit and the question becomes: "which multiple
of 9 has only 1's and 0's?
That answer is of course 111.111.111 (the smallest answer), because it
must be divisible by 9.
Since we dropped 3 zeros, the final answer is indeed (looking at Basil's
solution) 111.111.111.000
Solution of Basil was very nice, I've learnt something!
Wiebe Veldhuis