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.

What is the smallest whole number that, when divided by 2, leaves a remainder of 1; when divided by 3, leaves a remainder of 2; and so on, up to leaving a remainder of 9 when divided by 10?

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