Brain Teasers

1. Consider the string of six numbers from 1 to 6. Can you place them in the circles set in a triangular pattern so that the numbers on each side add up to the same sum?
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Now take the numbers from 1 to 9. Can you place them in the larger triangular pattern so that each side again sums up to the same number?
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2. Sudoku

You must all have seen the popular game of Sudoku. There are 9 rows and 9 columns with 81 little squares in all. Some of the squares are filled. The aim of the game is to fill in the blank squares with numbers from 1 to 9 so that no number repeats in either a row or a column or a sub-square. A sub-square is a collection of 9 little squares with three rows and three columns so there are 9 sub-squares in the big Sudoku square.
Let us think of the simpler problem of a 4 X 4 Sudoku. As shown in the figure, there are 4 rows, 4 columns and 4 sub-squares which are of size 2 by 2 each (as denoted by the dark lines). Here the aim is to fill in the numbers from 1 to 4 with no repeats in row, column or sub-square.
The problem: One sub-square of the Sudoku is correctly filled, with no other entries. Can you correctly complete the Sudoku according to the rules? What about the case of a 9 X 9 Sudoku?