#puzzle
Without computer assistance, find five different sets of three positive integers {k, m, n}
such that k < m < n and
(1/k)+(1/m)+(1/n) = 19/84

Since this involves fractions the gcd of the denominators k,m,n can be considered to be 84.
So multiplying by 84 we can write this as a + b +c = 19 where
a = 84/k
b = 84/m
c = 84/n
and a, b, c must lie in the factors
1,2,3,4,6,7,12,14,21,28,42,84
Moreover a > b > c for k < m < n
By eliminating a few of these, we can say 'a' could start from 7,12 or 14.
We find two such pairs  for (a,b,c)
12, 6, 1  which implies k,m,n is 7,14,84
12, 4, 3  which implies k,m,n is 7, 21, 28
Similarly when a is 14, we get
14, 4, 1  which implies k,m,n is 6, 21, 84
14, 3, 2  which implies k,m,n is 6, 28, 42
Since we tried k = 6, 7, we can try k =5 and use a gcd of 420
which gives us k,m,n as 5, 60, 105

#codingexercise
In a rowwise and columnwise sorted matrix, enumerate the elements in ascending order
There is a front that moves from the top left corner to the bottom right. Element along the front are guaranteed to include the minimum. Since the front only moves one cell down or to the right, the element along the zig zag shape of the front are easy to enumerate to pick out the minimum at any step.