4. Seven people are suspected of theft:

Alex, a brown-haired man with blue eyes;

Boris, a blonde man with green eyes;

Chris, a blonde man with brown eyes;

Denise, a blonde woman with brown eyes;

Detectives Helga, Ingrid, and Julius know that one of the suspects is the thief. After doing some detective work, they share the following information in a dialogue.

Helga: "I know the eye and hair color of the thief, but I don't know who it is."

Ingrid, who hasn't heard Helga, says:

"I know the hair color and gender of the thief, but I don't know who it is."

Julius finally says:

"At first, I only knew the gender, but after your statements, I know who the thief is."

The detectives are telling the truth. Who is the thief?
B4. Denise First, we look at Helga's statement. Alex and Eva have the same eye color and hair color, and Chris and Denise also have that. Boris, Felix, and Gaby, on the other hand, have a unique combination of eye and hair color. From Helga's statement, we can infer that Boris, Felix, and Gaby are not the thief, as Helga could have deduced this from their eye and hair color. Alex, Chris, Denise, and Eva, however, are still possible suspects because they do not have a unique combination of eye and hair color.

$\mathrm{Now}$ we look at Ingrid's statement. Alex and Felix have the same hair color and gender, as do Boris and Chris, and also Denise and Gaby. Only Eva has a unique combination of hair color and gender. From Ingrid's statement, we can infer that Eva is not the thief, as Ingrid would have known that Eva was the thief otherwise. The other six are not excluded as suspects by Ingrid's statement.

Based on the statements of Helga and Ingrid, Julius can conclude that Boris, Eva, Felix, and Gaby are not the culprit. Without additional information, however, Alex, Chris, and Denise can still all be the culprit. Julius has an extra piece of information, the gender of the culprit, with which he can now determine which of the three is the culprit. If the culprit were a man, he could only conclude that it was either Alex or Chris. The culprit must therefore be a woman, namely Denise.