a mathematical curiosity that maybe could help the puzzle:
all numbers even that respects this succession 4,10,16,22,28,34,40,46.....To infinity
divided by 3
plus the sum of +1 to the same number divided by 3, results in an integer, odd number.
target = 100
target_2 = 100+1 #= 101
t1= target//3 #= 33.333333333333336
t2= target_2//3 #= 33.666666666666664
r= t1+t2 # = 67