# Home city and Visited City

P, R, S, T, U and V are six colleagues who work for Fan Inc. headquartered at USA. Each of them lives in a different city that is one out of P, R, S, T, U and V, not necessarily in that order. Their organization has assigned each of them for a field visit in one of these six cities such that neither of them will be sent to the city where they live. The following points are known.

— S will visit the city where T lives. — U will visit P. — V is from T. — R and U will visit each other's home city. — P's home city will be visited by the person who lives in R. — The person from S will visit T. — The initials of the name of each employee, his home city, his visiting city and the name of the person who lives in that visiting city are different.

Source : Me

Which city will V visit? S U R Cannot be determined

Please tell the approach.

## 1 Answer

• First step : create an empty grid with tree columns, people, habitation city and working city

  people   |habitation city|working city
---------|---------------|------------
P        |               |
R        |               |
S        |               |
T        |               |
U        |               |
V        |               |


We can know fill the grid with statements

• Statement n°2 : "U will visit P."

simple statement

  people   |habitation city|working city
---------|---------------|------------
P        |               |
R        |               |
S        |               |
T        |               |
U        |               |
V        |               |


• Statement n°3 : "V is from T."

simple statement

  people   |habitation city|working city
---------|---------------|------------
P        |               |
R        |               |
S        |               |
T        |               |
U        |               | P
V        | T             |


• Statement n°4 : "R and U will visit each other's home city."

This means R's home city is U's working city

  people   |habitation city|working city
---------|---------------|------------
P        |               |
R        | P             |
S        |               |
T        |               |
U        |               | P
V        | T             |


• Statement n°7 : "The initials of the name of each employee, his home city, his visiting city and the name of the person who lives in that visiting city are different."

This means U's home city can't be P (already working city), R (the name of the person who lives in that visiting city), T (already used by V), and only leaves us S or V

  people   |habitation city|working city
---------|---------------|------------
P        |               |
R        | P             |
S        |               |
T        |               |
U        | S/V           | P
V        | T             |


• Statement n°6 : "The person from S will visit T."

As U already visit P, he can't be from S

  people   |habitation city|working city
---------|---------------|------------
P        |               |
R        | P             |
S        |               |
T        |               |
U        | V             | P
V        | T             |


• Statement n°4 : "R and U will visit each other's home city."

R visit V

  people   |habitation city|working city
---------|---------------|------------
P        |               |
R        | P             | V
S        |               |
T        |               |
U        | V             | P
V        | T             |


• Statement n°7 : "The initials of the name of each employee, his home city, his visiting city and the name of the person who lives in that visiting city are different."

Add all combinations

  people   |habitation city|working city
---------|---------------|------------
P        | R/S/U         | R/S/T/U
R        | P             | V
S        | R/U           | R/T/U
T        | R/S/U         | R/S/U
U        | V             | P
V        | T             | R/S/U


• Statement n°1 : "S will visit the city where T lives."

S can't visit T as T can't live in T, T can't live in S as S can't work in S

  people   |habitation city|working city
---------|---------------|------------
P        | R/S/U         | R/S/T/U
R        | P             | V
S        | R/U           | R/U
T        | R/U           | R/S/U
U        | V             | P
V        | T             | R/S/U


• Statement n°7 : "The initials of the name of each employee, his home city, his visiting city and the name of the person who lives in that visiting city are different."

S can't be the home city of S neither T, so S is the home city of P. P can't work at S anymore. Also, only P can work at T

  people   |habitation city|working city
---------|---------------|------------
P        | S             | T
R        | P             | V
S        | R/U           | R/U
T        | R/U           | R/S/U
U        | V             | P
V        | T             | R/S/U


• Statement n°5 : "P's home city will be visited by the person who lives in R."

P's home city is S. S can't work in S, that means T visit S and live in R. Therefore, S live in U

  people   |habitation city|working city
---------|---------------|------------
P        | S             | T
R        | P             | V
S        | U             | R/U
T        | R             | S
U        | V             | P
V        | T             | R/U


• Statement n°1 : "S will visit the city where T lives."

S will visit R

  people   |habitation city|working city
---------|---------------|------------
P        | S             | T
R        | P             | V
S        | U             | R
T        | R             | S
U        | V             | P
V        | T             | U


Final answer

V will visit U

• Great Reasoning and Explanation. Thanks for your effort. @kepotx – sam Oct 22 '18 at 0:35