# Blog

## Archive

Show me a random blog post**2018**

### Jul 2018

World Cup stickers 2018, pt. 3Mathsteroids

### Jun 2018

World Cup stickers 2018, pt. 2### May 2018

A bad Puzzle for Today### Apr 2018

Building MENACEs for other games### Mar 2018

A 20,000-to-1 baby?World Cup stickers 2018

### Jan 2018

*Origins of World War I*

Christmas (2017) is over

**2017**

**2016**

**2015**

**2014**

**2013**

**2012**

## Tags

folding paper folding tube maps london underground platonic solids london rhombicuboctahedron raspberry pi weather station programming python php inline code news royal baby probability game show probability christmas flexagons frobel coins reuleaux polygons countdown football world cup sport stickers tennis braiding craft wool emf camp people maths trigonometry logic propositional calculus twitter mathslogicbot oeis matt parker pac-man graph theory video games games chalkdust magazine menace machine learning javascript martin gardner noughts and crosses reddit national lottery rugby puzzles game of life dragon curves fractals pythagoras geometry triangles european cup dates palindromes chalkdust christmas card ternary bubble bobble asteroids final fantasy curvature binary arithmetic bodmas statistics error bars estimation accuracy misleading statistics pizza cutting captain scarlet gerry anderson light sound speed manchester science festival manchester dataset a gamut of games hexapawn nine men's morris draughts chess go radio 4 data map projections aperiodical big internet math-off sorting**2014-05-26**

## World Cup stickers

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