When someone tells you to “play the numbers” in a Logic Game, does your mind go blank, or even worse, to some kind of ill-conceived gambling scheme? If you’re not yet comfortable with playing the numbers, then you’re in luck (with your LSAT aspirations at least). Playing the numbers is mainly going to be a method deployed on overbooked and underbooked logic games. It’s a way to determine the parameters of the game (the smallest and largest numbers you can use while applying all of the game’s rules). This allows you to narrow down the game to a few possible scenarios. Let’s look at a couple examples to see how you would “play the numbers” in an actual game.
Here’s a setup for a logic game: Alexis is having her bachelorette party in Vegas, but she only has three hotel rooms for herself and her seven closest friends: Becky, Carly, Daisy, Emily, Fanny, Gaby and Haley. Each room can sleep up to two people. Alexis must go on the trip, but the invitations for the friends have not been decided.
Now, if the game setup requires us to figure out the possible combinations of people to rooms (making it a a grouping game), we can play the numbers to make a deduction about the limits already set out in this game. To start, we know this game is overbooked, because there are literally too many people for the number of hotel rooms that are booked. It’s also unstable, in that we don’t even know how many people will be attending the trip. That’s where you can “play the numbers” by figuring out the lowest and highest number of people who may be able to stay in the hotel rooms. In this case, the lowest possible number would be 1, with Alexis on her own at the word’s saddest bachelorette party. This would mean 1 person in one room, and 0 in the other two rooms. Now for the highest possibility, we look at the maximum number of slots available across all of the groups. In this case, each of the three rooms can accommodate 2 people, making 6 the greatest number of people allowed across all groups. In between those two extremes, we could have 2 people (with either them sharing the room, with the other rooms empty, or each person getting a room of her own), or 3 people, with either 2 in a room and 1 in another, or each getting her own room), or 4 people (with 2 per room, or 2 sharing one room and 2 getting a private room), or 5 people (with 2 in one room, 2 in another, and 1 getting a private room).
Time to step up the difficulty with Game #2:
Now, Alexis and the 5 friends who made it on her bachelorette trip (specifically, the friends with names beginning with B-F) are going to see Britney Spears’ live concert in Las Vegas. Luckily, all of the women have tickets this time. However, due to some tension within the group, not all of the friends are willing to attend the concert together: Alexis (A) is going no matter what. Carley (C) and Emily (E) each say they will definitely go, but only if the other one isn’t going. Neither Carly (C), Daisy (D) or Fanny (F) will go to the concert if Becky (B) goes. In this game, we would get some further rules to figure out who can sit where, but to even begin, we need to play the numbers to figure out how many of the friends can go to the concert, based on the rules we have above (making this a combo In & Out/Ordering Game). Since C and E won’t attend the concert together, we’re already down to five attendees. However, based on the rule that C, D and F would only attend if B does not attend, we know that the highest total of attendees for the six reserved seats is just four people: A, C, D and F. And what’s the lowest number of attendees? We have A, plus either one of C or E, adding up to a minimum two attendees in six possible seats.
Playing the numbers is really about taking the seemingly daunting possibilities presented by many Logic Games and finding the actual parameters of the game based on the rules provided. It can be applied to figure out: how many slots your players will occupy in an underbooked ordering game, how many players will occupy a given spot in an overbooked ordering game, how many groups your players will join in an underbooked stable grouping game, how many players from each subgroup will join the in group on an in & out game with multiple subgroups, or how many slots the groups will have on an unstable grouping game. It’s a type of deduction that can save a lot of time and even reveal other deductions to help you bring some logic to the games on your LSAT.