Climbing stairs
When I go up my stairs in a hurry, I take some steps two-at-a-time.
This morning, I climbed my thirteen steps in this pattern: 1, 2, 1, 2, 1, 1, 2, 1, 2.
Yesterday the pattern was 1, 1, 1, 1, 1, 1, 2, 2, 1, 2.
How many days do you think I can go before I have to repeat a pattern?
First I thought I should find a pattern from the easiest ones to get the pattern for the harder ones (climbing up 1 and 2 at a time). SO…
What are the least possible steps I need to take to get up 13 stairs when each step can be 13 stairs high?
And the answer was easy: 1
What are the least possible steps I need to take to get up 13 stairs when each step can be 12 stairs high?
And the answer wasn’t too hard either: 2
What are the least possible steps I need to take to get up 13 stairs when each step can be 11 stairs high?
Starting to get hard, but after few seconds of thinking, I’ve got the answer: 5, you can see the answer has gone up dramatically. Still, the pattern isn’t too recognisable.
What are the least possible steps I need to take to get up 13 stairs when each step can be 10 stairs high?
The answer is probably: 12
Typing up this sequence in the Internet, I found a sequence called the Pell numbers, and it was said that the next number in the sequence is 29.
To make it more reliable, we will do another question
What are the least possible steps I need to take to get up 13 stairs when each step can be 9 stairs high?
And the answer is 29.
So the sequence is pell number. But what is pell number, pell number is the number times 2 then add the previous number.