The Panini Formulas

The Panini sticker book for the upcoming UEFA Euro 2016 football tournament features 680 stickers this time. We can calculate how many sticker we need to buy to fill the album by using the amazing (due to its relationship to music and architecture) harmonic series formula:

Latex formula

Buying 4829 stickers, it will give me 4149 stickers to swap, assuming that stickers are evenly distributed. If we take into account that stickers are not sold separately but in packs of 5 stickers, the result is slightly different.

Having bought my first 160 stickers today, I have 3.3% of these already, caught in the coupon collector’s problem. We can calculate the probable duplicates I will have from these 160 stickers by:

Latex formula

and I ended up with 17 duplicates, which is nearby.