Source: Recent puzzle reading (still looking for the actual source.)
Find four 3-digit numbers which have the same first digit, such that
the sum of all four numbers is divisible by three of them.
For each n (4<=n<=7), can you find a set of n+1 integers, all
the same length and beginning with the same digit, such that their sum
is divisible by n of them? Try to minimize the sum.
For each n (2<=n<=7),
find the smallest integer M, such that when you divide M evenly by
k, k+1, ..., k+n-1, you get n integers, all beginning with the same
digit. You can choose k in each case.
Mail to Ken