How to Solve Logic Problems
The simplest (not to say easiest nor necessarily quickest) way to solve these problems is with a table like the one below. Let's look at an example and work it through, shall we?Four brothers go to a dance.
The first thing to do is to set up a chart showing all the possibilities, and then take out the ones we know are wrong. (As Sherlock Holmes would say, "Once one rules out all the impossibilities, whatever is left - however improbable it may seem - will be the truth." We're going to rule out the impossibilities one by one.)
- As they leave, each one of the brothers accidentally takes a hat belonging to one of his brothers and a coat belonging to yet another brother.
- Maurice took the coat belonging to the brother whose hat was taken by Adiel, while
- Adiel's coat was taken by the brother who took Maurice's hat.
- Art took Jerome's hat.
- Whose coats and hats did Maurice and Adiel take?
No brother took his own hat or coat, so the first thing we do is red out those boxes.
Hat |
Hat |
Hat |
Hat |
Coat |
Coat |
Coat |
Coat |
||
Maurice
|
|||||||||
Adiel
|
|||||||||
Art
|
|||||||||
Jerome
|
We know that Art took Jerome's hat, so we check that box and red out the other hats and coats for Art. This also means that Art didn't take Jerome's or his own coat, so we red those boxes, as well as the other brothers' boxes for Jerome's hat.
Hat |
Hat |
Hat |
Hat |
Coat |
Coat |
Coat |
Coat |
||
Maurice
|
|||||||||
Adiel
|
|||||||||
Art
|
|
||||||||
Jerome
|
Adiel's coat was taken by the Maurice hat-taker, who isn't Art, so Art took Maurice's coat (because that's the only other coat left for him). Now we check that box, as well as redding out the boxes for the other brothers with Maurice's coat.
Maurice's
HatAdiel's
HatArt's
HatJerome's
HatMaurice's
CoatAdiel's
CoatArt's
CoatJerome's
Coat Maurice Adiel ArtX X JeromeAdiel didn't take his own coat, so he also didn't take Maurice's hat (they were taken by the same brother) - we red out that box now.
Maurice's
HatAdiel's
HatArt's
HatJerome's
HatMaurice's
CoatAdiel's
CoatArt's
CoatJerome's
Coat Maurice Adiel ArtX X JeromeThis means that Adiel took Art's hat (because the others are already accounted for, except his own), so he didn't take Art's coat, so he took Jerome's. We check and red the appropriate boxes.
Maurice's
HatAdiel's
HatArt's
HatJerome's
HatMaurice's
CoatAdiel's
CoatArt's
CoatJerome's
Coat Maurice AdielX X ArtX X JeromeThis leaves only Adiel's hat for Maurice, so Jerome took Maurice's hat. Maurice took Adiel's hat, so he didn't take Adiel's coat, so he took Art's coat (the only one left for him). That means that Jerome took Adiel's coat, since it's the only one left for him. Go ahead and check and red those boxes.
Maurice's
HatAdiel's
HatArt's
HatJerome's
HatMaurice's
CoatAdiel's
CoatArt's
CoatJerome's
Coat MauriceX X AdielX X ArtX X JeromeX X See how simple that was? Aren't you glad you went through this exercise?