01 Apr March Puzzler
DIGITAL AGENT ENGINEERS SOLVE COMPLEX PUZZLES FOR OUR CUSTOMERS EVERY DAY. CAN YOU SOLVE THE PUZZLE WE CREATED FOR YOU?
It’s March and everyone at Digital Agent has abandoned their 2019 New Year’s resolution. Everyone, that is, except for our leader, Howard! Howard has been taking the stairs to our 5th floor suite at least 3 times every weekday. Today, one of our engineers brought their son’s creepy toy snake to the office. The team decided to wait for Howard to leave for his regular climb, sneak into the stairwell, and plant the snake as a prank. And, of course, our accountant turned this into a math problem.
If a flight has 8 stairs, and Howard takes either 1 or 2 stairs with each stride, how many different ways can he reach the top if he can’t step on the 5th (snake-occupied) stair? (For example, one way is 11122, while another is 21211)
There were two ways to interpret this problem (are you starting on stair 1, or on the ground?), so we’re posting solutions for both. Since Howard can either take 1 or 2 stairs per stride, the number of ways to get to stair 8 is the number of ways to get to stair 7 plus the number of ways to get to stair 6. This pattern works for any stair we choose, so we can count up the total number of combinations by starting at the bottom and working our way up. Take a look at the pictures!
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