# Deductive Reasoning Logical Problem

Deductive Reasoning Logical Problem Solution - 26 August

There are 4 big houses in my home town.

They are made from these materials: red marbles, green marbles, white marbles and blue marbles.

* Mrs Jennifer's house is somewhere to the left of the green marbles one and the third one along is white marbles.
* Mrs Sharon owns a red marbles house and Mr Cruz does not live at either end, but lives somewhere to the right of the blue marbles house.
* Mr Danny lives in the fourth house, while the first house is not made from red marbles.

Who lives where, and what is their house made from ?

Solution
From, left to right:
#1 Mrs Jennifer - blue marbles
#2 Mrs Sharon - red marbles
#3 Mr Cruz - white marbles
#4 Mr Danny - green marbles

If we separate and label the clues, and label the houses #1, #2, #3, #4 from left to right we can see that:
a. Mrs Jennifer's house is somewhere to the left of the green marbles one.
b. The third one along is white marbles.
c. Mrs Sharon owns a red marbles house
d. Mr Cruz does not live at either end.
e. Mr Cruz lives somewhere to the right of the blue marbles house.
f. Mr Danny lives in the fourth house
g. The first house is not made from red marbles.

By (g) #1 isn't made from red marbles, and by (b) nor is #3. By (f) Mr Danny lives in #4 therefore by (c) #2 must be red marbles, and Mrs Sharon lives there.

Therefore by (d) Mr Cruz must live in #3, which, by (b) is the white marbles house.

By (a) #4 must be green marbles (otherwise Mrs Jennifer couldn't be to its left) and by (f) Mr Danny lives there.

Which leaves Mrs Jennifer, living in #1, the blue marbles house. QED.