Raghu is fond of his grandfather's torch. He starts playing with it. He presses the switch once and the light turns ON. He presses it a second time and the light turns OFF. He presses the switch a third time and the light turns ON. He keeps doing this several times. Will the torch be ON or OFF after the 23rd press? How do you know? For what number of presses will the torch be ON? For what number of presses of the switch will the torch be OFF?
After the 23rd press, the torch will be ON.
Pattern: Odd-numbered presses (1st, 3rd, 5th, 7th...) turn the torch ON. Even-numbered presses (2nd, 4th, 6th, 8th...) turn the torch OFF.
Since 23 is an odd number, ∴ The torch will be ON after the 23rd press.
Torch will be ON after presses: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25... (all odd numbers)
Torch will be OFF after presses: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24... (all even numbers)
Explanation
The chapter connects this problem to even and odd numbers. The torch alternates between ON and OFF with each press. Starting OFF, press 1 makes it ON, press 2 makes it OFF, and so on. Odd-numbered presses result in ON state, even-numbered presses result in OFF state.
Solution Steps
Step 1: Identify the pattern: Press 1 = ON, Press 2 = OFF, Press 3 = ON, Press 4 = OFF...
Step 2: Recognize that odd-numbered presses turn the torch ON
Step 3: Recognize that even-numbered presses turn the torch OFF
Step 4: Since 23 is an odd number, the torch will be ON after the 23rd press
Step 5: Torch ON: odd presses (1, 3, 5, 7...). Torch OFF: even presses (2, 4, 6, 8...)