Daycare Illness Bingo (it’s not just a game)!
Our child recently started daycare, which means the immune systems of our household are about to be given a pretty dramatic workout. To try to derive a little more fun from the situation, I went looking for a daycare illness bingo card. We’re an English-French bilingual household raising an English-French bilingual child and, while I saw a few passable examples of daycare bingo cards, I really wanted to find something bilingual. No dice.
So, I made my own. And I got carried away and built a bingo card generator. And then I got carried away again. Because of course I did.
The bingo card generator is built in Excel, and populated with a list of at least 24 common childhood illnesses. There is a randomizer¹ that then generates bingo cards based on the items in the list.
(As a matter of fact, the bingo card doesn’t even have to be for daycare illnesses — you could put anything you want in the list of possible bingo card entries. Use it for the predictable jargon spewed during election campaigns, or whatever.)
Every trip to daycare is a spin of the wheel! Get your markers ready and have fun!
Here’s how it works.
The Excel file contains a BINGO CARD Sheet that contains a randomly-generated Bingo Card, which has space for 24 entries:
The file also contains a backend Sheet, where the heavy lifting is done:
Column A contains the list of possible entries in the Bingo Card (in this case, childhood illnesses).
Column B contains unique randomly-generated integers with range equal to the number of entries in Column A by using the following function:
=INDEX(UNIQUE(RANDARRAY(G3^2,1,1,G3,TRUE)),SEQUENCE(G3))
Where G3 is a cell containing:
=COUNTA(A:A)
G3 simply returns the number of entries in Column A.
Defining the UNIQUE RANDARRAY function in Column B in this way lets us have a number of entries greater than the number of spaces in the bingo card. The bingo card would then contain a subset of that list. In other words, we could have 100 possible childhood illnesses (there but for the grace of modern epidemiology go we) and the bingo card would contain 24 of them at random.
Finally, Cell D1 contains:
=INDEX($A:$A,B1,1)
D2 contains “=INDEX($A:$A,B2,1)”, D3 contains “=INDEX($A:$A,B3,1)”, and so on. This function pulls everything together by taking the unique random integers in Column B and using them to pull entries from Column A.
The bingo card itself is simply a rearranged version of the information in Column D.
The number of possible Bingo Cards is based on permutations of the entries in Column A — it’s a permutation if the order matters, it’s a combination if it doesn’t.
For 24 entries where we can’t use the same entry twice, the number of possible Bingo Cards is:
n! = 24!
= 24 * 23 * 22 * 21 * … * 3 * 2
= 620 448 401 733 239 439 360 000
That’s on the order of 10²³ (take that, Avogadro!). The number gets even bigger when we pick a subset of 24 entries from a larger set of entries. Say we want to add just one more entry to our list of illnesses, bringing the total to 25. Here, the number of 24-entry Bingo Cards that can be made climbs to:
P(n,r) = n! / (n-r)!
P(25,24) = 25! / (25–24)!
= 25! / 1! = 25! / 1 = 25!
= 15 511 210 043 330 985 984 000 000
G6 contains a function to compute the number of possible permutations given of a 24-entry subset drawn from an arbitrarily long list of possible entries:
= FACT(G3)/FACT(G3–24)
Just for fun, the number of ordered 24-item subsets that could be picked from a 26-item list is 201 645 730 563 302 817 792 000 000. That’s on the order of 10²⁵. To put that in context, there may only be about 1 000 000 000 000 000 000 000 000 stars (or 10²⁴) in the universe.
¹Pseudorandom. I know.
Note: I will be upset if it turns out that it was a mistake to leave out the measles.
