Please show us what you have tried and exactly where you are stuck.We have 6 levels of cards - levels 1, 2, 3, 4, 5 and 6.
If 5 cards of one level = 2 of the next level
and 3 cards of one level = 1 of the next level ,
how many level 1 cards minimum would it take to get to a level 6 card?
By my calculations it would take 125 level 1 cards minimum to get to level 6. I'm not sure if that's correct though so I would appreciate it if somebody double checks this.Please show us what you have tried and exactly where you are stuck.
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Please share your work/thoughts about this problem.
To get 1 six you would need 3 5's.I think you only need 98 level 1 cards to get level 6. Assuming the worse rate of 2.5cards of the previous level to get 1 of the next.
We can write a recursive formula:
[math]A_{n}=A_{n-1}\cdot\frac{2}{5}[/math]
To get 1 six you would need 3 5's.
To get 3 5's you would need 8 4's (5 to get two and 3 to get 1 more).
To get 8 4's you would need 20 3's.
To get 20 3's you would need 50 2's.
To get 50 2's you would need 125 1's.
Level number of cards
6 1
5 3
4 8
3 20
2 50
1 125