Question

Caden, Jacob, Lucas, and Michael, whose last names are Armstrong, Boothe, Gardner, and Robinson, live in four houses in a row.

From the clues below, find each person’s full name and house position (with house number 1 at the left).

1. Michael doesn’t live next door to Lucas.
2. Robinson’s house is after Gardner’s and before Michael’s.
3. Boothe’s house is just before Armstrong’s.
4. Lucas’ house, which is not first, is somewhere to the left of Caden’s.

Answer 1

Jacob Gardner - Lucas Robinson - Caden Boothe - Michael Armstrong

Step-by-step explanation:

According to clue 4, Lucas's house is not the first, and he has a house on his right, so it can only be house 2 or house 3. Therefore, Caden's house (which is on the right right of Lucas's), it can only be house 3 or house 4.

In turn, track 1 says that Michael's house is not next to Lucas's, so it can be 1 (if Lucas's house is 3) or 4 (if Lucas's house is in 2).

Track 2 says that there is a house before Michael's, which eliminates the possibility that Michael's house is number 1 (there would be no previous house). Thus, in addition, Lucas's house turns out to be 2 (Michael's house is not next door) and Caden's is 3, while Jacon's is house 1.

Jacob - Lucas - Caden - Michael

In turn, regarding surnames, clue 2 says that Robinson's house is after Gardner's and before Michael's. Thus, Robinson can be the last name of Jacob or Lucas, and Gardner that of Lucas or Caden. Now, since Boothe's house is just before Armstrong's, the order would be as follows:

Jacob Gardner - Lucas Robinson - Caden Boothe - Michael Armstrong