Infosys Company Numerical Ability Geometry

If an equilateral triangle is partitioned into n convex polygons, determine the maximum number of edges present in the resulting figure. The diagram below shows a partitioning into 3 polygons with 8 edges (which is not necessarily the maximum) and 6 vertices.
You may find a result of Euler applicable to this problem. The result states that if a polygon is partitioned into n polygons, then v-e+n=1 where v is the number of vertices and e is the number of edges in the resulting figure.

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Infosys Other Question

The following game is played on a rectangular chessboard of size 5*7 (i.e. there are 5 rows of squares each row containing 7 squares). Initially a number of coins are randomly placed on some of the squares, no square containing more than one coin. A complete move consists of moving every coin from the square containing it to another square subject to the following rules
i. every coin may be moved one square up or down, or left or right of the square it occupies to an adjacent square;
ii. if a particular coin is moved up or down as part of a complete move, then it must be moved left or right in the next complete move;
iii. if a particular coin is moved left or right as part of a complete move, then it must be moved up or down in the next complete move;
iv. at the end of each complete move, no square can contain two or more coins.

The game stops if it becomes impossible to make a complete move.

I. Show that if initially 25 coins are placed on the board, then the game must eventually stop.

II. Show that it is possible to place 24 coins on the board in such a way that the game could go on forever. During the testing of drug the result were found to be 85% positive in the first phase of 100 tests and 55% positive of second phase.If the overall results were 75% positive.what was the total number of tests conducted in first phase and second phase?