Answer / guest

The formula to find number of diagonals (D) given total
number of vertices or sides (N) is

N * (N - 3)

D = -----------

2

Using the formula, we get

1325 * 2 = N * (N - 3)

N2 - 3N - 2650 = 0

Solving the quadratic equation, we get N = 53 or -50

It is obvious that answer is 53 as number of vertices can
not be negative.

Alternatively, you can derive the formula as triange has 0
diagonals, quadrangel has 2, pentagon

has 5, hexagon has 9 and so on......

Hence the series is 0, 0, 0, 2, 5, 9, 14, ........ (as
diagram with 1,2 or 3 vertices will have 0

diagonals).

Using the series one can arrive to the formula given above.

A number. if it is divided by 2 reminder 1, if it is divided by 3 reminder 1, if it is divided by 4 reminder 1, if it is divided by 5 reminder 1, if it is divided by 6 reminder 1, if it is divided by 7 reminder 1, if it is divided by 8 reminder 1, if it is divided by 9 reminder 1, if it is divided by 10 reminder 1, and if it is divided by 11 reminder 0. its greater then 100. which is that number. this puzzle has been appeared in one of written test(aptitude for 20 marks).

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