mscroggs.co.uk
mscroggs.co.uk

subscribe

Blog

 2014-05-26 
With the FIFA World Cup approaching, sticker fans across the world are filling up their official Panini sticker books. This got me wondering: how many stickers should I expect to need to buy to complete my album? And how much will this cost?

How many stickers?

There are 640 stickers required to fill the album. The last 100 stickers required can be ordered from the Panini website.
After \(n\) stickers have been stuck into the album, the probability of the next sticker being the next new sticker is:
$$\frac{640-n}{640}$$
The probability that the sticker after next is the next new sticker is:
$$\frac{n}{640}\frac{640-n}{640}$$
The probability that the sticker after that is the next new sticker is:
$$\left(\frac{n}{640}\right)^2\frac{640-n}{640}$$
Following this pattern, we find that the expected number of stickers bought to find a new sticker is:
$$\sum_{i=1}^{\infty}i \left(\frac{640-n}{640}\right) \left(\frac{n}{640}\right)^i = \frac{640}{640-n}$$
Therefore, to get all 640 stickers, I should expect to buy:
$$\sum_{n=0}^{639}\frac{640}{640-n} = 4505 \mbox{ stickers.}$$
Or, if the last 100 stickers needed are ordered:
$$\sum_{n=0}^{539}\frac{640}{640-n} + 100 = 1285 \mbox{ stickers.}$$

How much?

The first 21 stickers come with the album for £1.99. Additional stickers can be bought in packs of 5 for 50p or multipacks of 30 for £2.75. To complete the album, 100 stickers can be bought for 25p each.
If I decided to complete my album without ordering the final stickers, I should expect to buy 4505 stickers. After the 21 which come with the album, I will need to buy 4484 stickers: just under 897 packs. These packs would cost £411.25 (149 multipacks and 3 single packs), giving a total cost of £413.24 for the completed album.
I'm not sure if I have a spare £413.24 lying around, so hopefully I can reduce the cost of the album by buying the last 100 stickers for £25. This would mean that once I've received the first 21 stickers with the album, I will need to buy 1164 stickers, or 233 packs. These packs would cost £107 (38 multipacks and 5 single packs), giving a total cost of £133.99 for the completed album, significantly less than if I decided not to buy the last stickers.

How many should I order?

The further reduce the number of stickers bought, I could get a friend to also order 100 stickers for me and so buy the last 200 stickers for 25p each. With enough friends the whole album could be filled this way, although as the stickers are more expensive than when bought in packs, this would not be the cheapest way.
If the last 219 or 250 stickers are bought for 25p each, then I should expect to spend £117.74 in total on the album. If I buy any other number of stickers at the end, the expected spend will be higher.
Fortunately, as you will be able to swap your duplicate stickers with your friends, the cost of a full album should turn out to be significantly lower than this. Although if saving money is your aim, then perhaps the Panini World Cup 2014 Sticker Book game would be a better alternative to a real sticker book.

Similar posts

World Cup stickers 2018, pt. 3
World Cup stickers 2018, pt. 2
World Cup stickers 2018
Euro 2016 stickers

Comments

Comments in green were written by me. Comments in blue were not written by me.
 Add a Comment 


I will only use your email address to reply to your comment (if a reply is needed).

Allowed HTML tags: <br> <a> <small> <b> <i> <s> <sup> <sub> <u> <spoiler> <ul> <ol> <li>
To prove you are not a spam bot, please type "c" then "o" then "s" then "i" then "n" then "e" in the box below (case sensitive):

Archive

Show me a random blog post
 2019 

Sep 2019

A non-converging LaTeX document
TMiP 2019 treasure punt

Jul 2019

Big Internet Math-Off stickers 2019

Jun 2019

Proving a conjecture

Apr 2019

Harriss and other spirals

Mar 2019

realhats

Jan 2019

Christmas (2018) is over
 2018 
▼ show ▼
 2017 
▼ show ▼
 2016 
▼ show ▼
 2015 
▼ show ▼
 2014 
▼ show ▼
 2013 
▼ show ▼
 2012 
▼ show ▼

Tags

realhats wool reuleaux polygons trigonometry go php graph theory fractals folding tube maps golden spiral radio 4 christmas polynomials final fantasy mathsjam machine learning manchester mathslogicbot harriss spiral european cup noughts and crosses error bars cross stitch bubble bobble plastic ratio captain scarlet london underground python weather station braiding manchester science festival stickers countdown football palindromes coins propositional calculus dates logic raspberry pi dragon curves light javascript accuracy chebyshev latex data pizza cutting talking maths in public london speed nine men's morris misleading statistics hats reddit royal baby frobel christmas card oeis interpolation game show probability platonic solids map projections binary martin gardner approximation menace a gamut of games draughts statistics the aperiodical twitter programming pac-man curvature game of life geometry dataset tmip games people maths big internet math-off hexapawn matt parker inline code asteroids cambridge estimation gerry anderson rugby bodmas news electromagnetic field ternary chalkdust magazine chess world cup puzzles craft tennis folding paper golden ratio triangles video games sound rhombicuboctahedron pythagoras sport national lottery sorting arithmetic books flexagons probability mathsteroids

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2019