mscroggs.co.uk
mscroggs.co.uk

subscribe

Blog

World Cup stickers

 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 "elbatnuocnu" backwards in the box below (case sensitive):

Archive

Show me a random blog post
 2020 

Mar 2020

Log-scaled axes

Feb 2020

PhD thesis, chapter ∞
PhD thesis, chapter 5
PhD thesis, chapter 4
PhD thesis, chapter 3
Inverting a matrix
PhD thesis, chapter 2

Jan 2020

PhD thesis, chapter 1
Gaussian elimination
Matrix multiplication
Christmas (2019) is over
 2019 
▼ show ▼
 2018 
▼ show ▼
 2017 
▼ show ▼
 2016 
▼ show ▼
 2015 
▼ show ▼
 2014 
▼ show ▼
 2013 
▼ show ▼
 2012 
▼ show ▼

Tags

polynomials puzzles reuleaux polygons interpolation people maths bodmas graphs accuracy dragon curves boundary element methods big internet math-off folding tube maps arithmetic final fantasy manchester science festival convergence data christmas books sport london underground matt parker sobolev spaces stickers weak imposition numerical analysis advent calendar hannah fry world cup preconditioning matrices golden ratio national lottery mathsteroids phd speed wool matrix of minors palindromes twitter gaussian elimination european cup reddit pythagoras radio 4 countdown game of life golden spiral pac-man map projections manchester sorting raspberry pi machine learning london game show probability approximation graph theory hats probability sound propositional calculus php plastic ratio chess mathslogicbot wave scattering inverse matrices inline code platonic solids harriss spiral rugby asteroids signorini conditions captain scarlet martin gardner pizza cutting dates dataset estimation go bubble bobble ternary binary finite element method chebyshev mathsjam nine men's morris programming royal baby weather station a gamut of games determinants simultaneous equations tmip tennis oeis braiding gerry anderson exponential growth news light data visualisation cambridge curvature hexapawn cross stitch error bars games draughts matrix of cofactors logs video games ucl electromagnetic field royal institution trigonometry noughts and crosses computational complexity flexagons the aperiodical fractals misleading statistics python craft rhombicuboctahedron geometry matrix multiplication coins folding paper javascript realhats frobel logic chalkdust magazine bempp triangles football statistics talking maths in public christmas card latex menace

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2012–2020