Brain Teasers and Puzzles

You have a 3-litre jug and a 5-litre jug, and as much water as you need. How do you measure out exactly 4 litres using only these two jugs?

This is a classic logic puzzle, sometimes used in finance and engineering interviews many years ago. It also was featured in the movie Die Hard with a Vengeance!

You may be familiar with Sudoku, a combinatorial number placement puzzle in which you fill in a 9×9 grid with digits such that each row, column, and 3×3 square contains all of the digits 1-9 exactly once.

You come across a Sudoku puzzle in which the initially populated numbers appear to be legal (no row, column, or square had the same number twice), but it is clear that trying to solve the puzzle would lead to an impossible arrangement of numbers – an unsolvable puzzle not because there is not enough information, but because it forces you into a contradictory/rule-breaking result. What is the smallest possible sum of the initial numbers?