A group of six people live in the same apartment building. On a particular occasion, they got together one day for lunch. As part of their conversation, they discovered that each one lived on a different floor and that the amount of rent paid by each one of them was all different. Two facts immediately emerged out of the luncheon meeting. The higher the floor , the higher was the rent. The rent paid by one of the six people was $525.

The details of the six people are furnished below ( albeit not necessarily in that order).

First Names: Alice, Paul, Denise, Fiona, Sandra, Joe.

Last Names: Ackers, Pryor, Davidson, Johnson, Stevens, Falkin.

Floor: 12th, 14th, 17th, 21st, 24th, 25th.

Using the clues given below, determine the full names of the six renters, the floor on which each resides, and the amount of rent they each pay.

1. Ms. Johnson lives between Denise and Ackers.

2. The highest rent is not paid by Falkin, Stevens or Paul. It is $175 more than that of the 17th floor.

3. Floor 21 is rented at $75 more than where Ackers lives and $50 less than what Alice pays.

4. Sandra pays $475 which is $175 less than Ms. Davidson.

5. Pryor’s rent is $50 higher than Alice’s rent and $100 more than the rent paid by Joe.

6. The rent at the 12th floor is $450. No one with the initial P or A ( in either their first names or their surnames) lives there.

7. Stevens’ rent is lower than Johnson’s.

(In reply to Solution by Dej Mar)

I get the same answer. Here's my reasoning.

1. Mrs Johnson, is female so does not have the male first names, also not denise, and lives between two
 floors, so not the topmost (25) or bottommost floor (12).
 Denise doesn't have the surname Ackers

2. Falkin, Stevens or Paul not on the top floor.

3. Ackers pays less rent than floor 21 and thus, lives below floor 21 (not 21, 24, 25). Alice pays more rent, and is on either floor 24 or 25. Because Ackers and Alice are on different floors, Alice cannot have the surname Ackers.

4. Sandra pays $475, so is not on the bottom floor ($450). Ms Davidson pays more than Sandara and so is on a higher floor than her (i.e. Sandra must be at least on floor 14, so Davidson on floor 17 or above.) As Davidson is a Ms, exclude male forenames.

5. Pryor's rent is $50 higher than Alice's. As Alice can be in either floor 24 or 25 (topmost), alice must be in floor 24 and Pryor in 25. Neither Alice nor Joe have Pryor as a surname. Paul does not pay the highest rent, and so does not have surname Pryor. Now we know Alice's floor, from pt. 3, rent on floor 21 is $50 less than rent on floor 24.

6. The lowest floor excludes Ackers and Paul because of their initials (Alice's and Pryor's have already been deduced.)

7. From pt. 6, rent at floor 25 (Pryor's) is $50 greater than rent at floor 24 (Alice's). From pt.2, the highest rent is also $175 higher than rent on floor 17. Thus Alice's rent is

f17 + 175 = f25 (pt.2)
f21 + 50 = f24 (pt. 3)
f24 + 50 = f25 (pt.5)

Thus, equating equations 2 & 3 gives
f21 = f25 - 100.
That is floor 21 rent is $100 less than the highest (Pryor's) rent. Pt.5 places Jo at floor 21.

We can rewrite all floors above floor 17 in terms of floor 17
f24 + 50 = f17 + 175, so f24 = f17 + (175-50) = f17 + 125
f21 + 50 = f17 + 125
so, f21 = f17 + 75

summarizing:
f21 = f17+75
f24 = f17+125
f25 = f17+175

We know that we have the rents $450 at the bottom followed by $475 and $525, meaning that we can try to place $525
at floors 17, 21, 24 or 25. Placing $525 at floor 21 gives floor 17 a rent of $450. As this is the same as floor 12, we know this cannot be correct, as the rent for each floor must increase (and the rents are all different.) Hence, $525 must be assigned to floor 17.

8. Rent $450 is paid on floor 12 and $525 is paid floor 17, then rent $475 (from pt. 4) must be paid on floor 14, and Sandra is on floor 14. Prior is on the top floor so Sandra does not have that surname.

All the rents for all the floors are then 450, 475, 525, 600, 650, 700.

9. Pt. 3, Ackers pays $75 less than floor 21, so that person is on floor 17.
10. Pt. 4, Ms Davisdon pays $650, which puts her on floor 24, and names her Alice.

11. We know that Ackers is not called Denise (pt. 1), and so Denise cannot be on floor 17.

12. We already know that Johnson cannot be on floors 12,17 (pt1), 24 (Davidson) or 25 (Prayor). That leaves 14 and 21. As Joe is on floor 21, and pt.1 states it is Ms. Jonhson, only floor 14 remains, naming her Sandara Jonhson.

13. pt. 7, Stevens' rent is lower than Johnson's (floor 14), so Stevens must be on floor 12. By elmination, Falkin must be on the remaining floor, 21, naming him Joe Falkin.

14. pt.1 Ms Jonhson lives between Denise and Ackers. Ackers is on 17, Johnson on 14, thus Denise must be on 12, naming her Denise Stevens.

15. This leaves only Fiona as a forname for Pryor, and then Paul as the remaining name for Ackers.

So the final outcome is

Denise Stevens, floor 12, pays $450 in rent
Sandra Jonson, floor 14, pays $475 in rent
Paul Ackers, floor 17, pays $525 in rent
Joe Falkin, floor 21, pays $600 in rent
Alice Davidson, floor 24, pays $650 in rent
Fiona Pryor, floor 25, pays $700 in rent

 

 

 

 

 

Posted by bumble on 2006-08-25 12:27:07