How to Solve the 12 Men on an Island Riddle from Brooklyn Nine-Nine

What is the “12 Men on an Island” riddle?

There are 12 men on an island. 11 of them weigh exactly the same amount, but the other is slightly heavier or lighter. You have a seesaw to measure their weights, but you can only use it 3 times. Find the odd man out and determine if they’re heavier or lighter than the others. In some variations of the riddle, it’s 12 balls or coins instead of men.

How to Solve the “12 Men on an Island” Riddle

Measure 2 groups of 4 for the first weighing. Assign each person a letter and split them into groups of 4, such as ABCD, EFGH, and IJKL. Place ABCD on one side of the seesaw and EFGH on the other side. If the seesaw balances, the ABCD and EFGH groups are the same weights, and the person with a different weight is in group IJKL. If the seesaw drops on the ABCD side, a person in the ABCD group is heavier or a person in the EFGH group is lighter. If the seesaw drops on the EFGH side, someone in the ABCD group is lighter or someone in the EFGH group is heavier.

If the seesaw was level… You now know the people in the first groups are all the same weight, so use them to check the group you left out. Weigh ABC on one side and IJK on the other side for your second weighing. If the seesaw balances, then L is the person with a different weight. For the third weighing, compare L and any other person on the seesaw. If L’s side of the seesaw drops, they’re heavier. If it rises, then they’re lighter. If the IJK side drops, then one of them is heavier. For your third weighing, weigh I on one side and J on the other. If the seesaw drops on one side, then that person is heavier. If the seesaw balances, then K is heavier. If the IJK side rises, then one of them is lighter. On the third weighing, weigh I on one side and J on the other. If the seesaw rises one side, that person is lighter. If the seesaw stays level, then K is lighter.

If the seesaw dropped on the ABCD side… Someone on the ABCD side is heavier or someone on the EFGH side is lighter. Place ABE on one side of the seesaw and use CDI on the other. This puts 2 potentially heavier and 1 potentially lighter person on one side, and 2 potentially heavier and 1 normal person on the other. If the seesaw balances, then all the people on it weigh the same, and the odd person out is in the FGH group. For the third weighing, compare the weights of F and G. If one side rises up, that person is lighter. If the seesaw balances, F and G are the normal weight, and H is lighter. If the seesaw drops on the ABE side, then either A or B is heavier, and everyone else is the same weight. For the third weighing, put A on one side and B on the other. Whichever side drops has the heavier person. If the seesaw drops on the CDI side, then C or D is heavier, or E is lighter. For the third weighing, compare C and D on the seesaw. If it stays balanced, then E is lighter. If the seesaw drops on one side, then that person is heavier.

If the seesaw dropped on the EFGH side… Someone on the EFGH side is heavier or someone on the ABCD side is lighter. Split the people into new groups so EFA is on one side of the seesaw and GHI is on the other side. If the seesaw balances, then the 2 groups weigh the same, and the lighter person is in the BCD group. For your third weighing, compare B and C on the seesaw. If the seesaw stays balanced, then D is the lighter person. If one end of the seesaw rises, the person on that side is lighter. If the seesaw drops on the EFA side, then E or F is heavier, and everyone else is the same weight. On the third weighing, put E and F on opposite ends of the seesaw. Whichever side drops has the heavier person. If the seesaw drops on the GHI side, then G or H is heavier, or A is lighter. Everyone else is the same weight. For the third weighing, place G and H on opposite sides of the seesaw. If it balances, then A is lighter. If either end of the seesaw drops, the person on that side is heavier.

How to Solve the 12 Men Riddle with Logic Patterns

Use the tilt of the seesaw to determine who's heavier or lighter. By arranging the men on the seesaw in particular patterns for each weighing, you can simply look at which way the seesaw tilts to determine which person is the odd one out and if they’re heavier or lighter. Use the following arrangements, and then compare your results to the table to determine which man weighs differently. First weighing: ABFH and CDEG (IJKL unweighed) Second weighing: ABGI and FHJK (CDEL unweighed) Third weighing: EFIK and BCHL (ADGJ unweighed) How does it work? Each weighing has 3 potential outcomes: tilting left (L), tilting right (R), or staying balanced (=). If you’re doing 3 separate weighings, then there are 3, or 27, unique combinations of results. For example, one set of results from the 3 weighings could be tilting left, left again, and then right, or LLR. It’s impossible to solve the riddle with the combinations LLL, RRR, or ===, so you can remove them. This leaves 24 possible combinations. There are 12 men, and each gets assigned 2 combinations: one if they’re heavier and its inverse if they’re lighter. For example, you can assign one man the LLR results as the heavier combo, and then use RRL as the lighter inverse. After assigning the possible results to each person, arrange the men so that anyone who has L listed for the first weighing is on the left side. Place anyone with an R on the right side. Do the same for the second and third weighings using the second and third outcomes in the set. For example, a man with the RLL combination will go on the right for the first weighing, and the left for the second and third weighings. This ensures that each person gets weighed and compared to the other men. Logic Pattern Solutions to the 12 Men Riddle First Weighing Second Weighing Third Weighing Odd Person Out Lighter or heavier? L L = A Heavier L L R B Heavier L = L C Lighter L = = D Lighter L = R E Lighter L R L F Heavier L R = G Lighter L R R H Heavier = L L I Heavier = L = J Lighter = L R K Lighter = = L L Lighter = = R L Heavier = R L K Heavier = R = J Heavier = R R I Lighter R L L H Lighter R L = G Heavier R L R F Lighter R = L E Heavier R = = D Heavier R = R C Heavier R R L B Lighter R R = A Lighter

How did the “12 Men on an Island” riddle get popular?

The riddle appeared on an episode of Brooklyn Nine-Nine. In season 2 of the TV show Brooklyn Nine-Nine, Captain Holt challenges his team to solve a brain teaser for a chance to win Beyoncé tickets. While no one is able to solve the riddle, they discover that Holt doesn’t even know the answer either.