I need help with a math formula for summer school project. Here's the challenge.

There are 249 individual cards.

Of these individual cards there are:
101 commons
60 uncommons
53 rares
15 mythics
20 basic lands with 5 unique cards with 4 different artwork per land
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249 cards

A pack of cards contains 15 cards. In the 15 cards, you receive the following:

1 rare
3 uncommon
11 common
1 land art

In 1 out of every 8 packs the rare will be a mythic.

In about 1 out of every 70 cards opened you'll receive a "foil" version of the card. So there's two version of every card.

So the challenge is this. Assuming there's 0 duplicates


How many packs do you have to open in order to open 1 of every card?

Answer: 68 boosters. 53(R) + 15 (M) = 68. Within the pack, 3(U) x 68 = 204 uncommons, 11(c) x 68 = 748 commons and 1(L) x 68 = 68 lands. 68 x 15 = 1020


How many packs do you have to open in order to open 1 of every foil version? How do I being to solve for this? I'm having troubles wrapping my head around it. What I've figured out so far is this.

1 out of 70 cards requires 4.666666666666667 packs. Lets even assume that's 0 duplicates in this as well. 4.666666666666667 packs times 248 cards = 1157.333333333333. However, in 3 sets of 4.666666666666667 = 14 packs. So the number of packs would decrease, right? How would this be expressed in a formula?

Tweaker