Question

Solve the following activity in pairs . Eldar uses a controller with a circuit to light 16 LED lamps which are labeled from 1 to 16 . When the controller a gives signal to a LED lamp , it changes its state (ON or OFF ) . In the beginning, all the LEDs are swi hed OFF . Eldar has found a sequence of lightning: On the 1st second controller lights ON all LED lamps . ( 1 .... 2 ... 3 .....) On the 2nd it lights ON the LEDs that are even in the circuit. ( 2 ... 4 ... 6 .... ) On 3rd second it lights every third LED in the circuit. ( 3...6...9...) And so it continues in similar way... Which LEDs must be switched ON after the 16th second​

Answer 1

Non of the LED lamps present will be switched on after the 16th second

Step-by-step explanation:

From the question, the operation of the controller with time are;

The LED lamp the controller lights up on the 1st second = All LED lamps

The LED lamps the controller lights up on the 2nd second = All even numbered LED lamps = Every other lamp with a number which is a multiple of 2

The LED lamps the controller lights up on the 3rd second = Every other LED lamp with a number which is a multiple of 3

Given that the LED lamps continues in that way, the LED lamps the controller lights up on the 16th = The 16th LED lamp which is a multiple of 16

Therefore, the LED lamp(s) the controller lights up after the 16th second = The 17th or more LED lamp = Non of the LED lamps present will be switched on after the 16th second