For n in {1,2,...,9}, find all n-digit positive integers, which are
(1) n-pandigital, i.e. formed from a permutation of the digits 1 to n, with no repeat digits; and
(2) k-divisible, i.e. for all k, k ≤ n, the integer formed from the truncated left most k digits is evenly divisible by k.
And for n=10, also find all 10-digit pandigitals with the same second condition.
Example: 2136547 almost qualifies, but fails for k=2.
2136547 is divisible by 7
213654 is divisible by 6
21365 is divisible by 5
2136 is divisible by 4
213 is divisible by 3
21 is not divisible by 2
2 is divisible by 1
I Draw the face of a clock numbered with roman numerals in the usual way. Explain how to draw 4 rays radiating from the center such that the sum of the numerals in each sector is 20.
II At what time are the two hands of a clock situated so that, reckoning in minutes from XII, one is exactly the square of the distance of the other?
III At what time between three and four o’clock is the minute hand the same distance from VIII as the hour hand is from XII?
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