# Robo challange

**Computer Science**Level 3

He has with him a number of coins placed horizontally from left to right. Some coins are placed with Head side up and some with Tail side up. The Robo takes one integer input at a time. For the given integer it flips the coins places at positions which is a multiple of the that integer.

The coins are assigned position as follows:

Leftmost coins is assigned position 1.

Coin placed next to leftmost coin is assigned position 2 and so on.

For example, if list of coins placed represented from left to right is 'HTHHHHHHHTTT' that means:

First coin is placed with Heads up.

Second coin with Tails up.

Third coin with Heads up and so on...

Then if Robo is given input **4**. The Robo will be flipping coins placed at 4th, 8th and 12th positions. The resulting position of coins would be 'HTH**T**HHH**T**HHT**H**'.

Your task is to find length of **shortest sequence of integers** you need to input through Robo to make him flip all coins to **Tail** side.

The initial arrangement of coins is:

'HTTHHTTHTHHTTHHTTTHTHHHHHTHHHTTHHHTTHTHHHTHTTHHHTTTHHHHHTTTHHHHHHTHHHTHHTTHTHTHTHTTTHHHHHHHTHHHHHHHT'

For example if initially the coins placed are as: "HHTHHT". The length of shortest sequence is **2** and the sequence could be [3, 1] or [1, 3]. Giving it 3 would make it: 'HHHHHH' and 1 would make it: "TTTTTT".