Outre Ornaments, Inc. sells baubles, gewgaws, and trinkets. While there, a customer spoke to three different salespeople.

1. The first salesperson the customer talked to told him that any 7 baubles together with any 5 gewgaws have the same value as any 6 trinkets.
2. The second salesperson he talked to told him that any 4 baubles together with any 9 trinkets have the same value as any 5 gewgaws.
3. The third salesperson he talked to told him that that any 6 trinkets together with any 3 gewgaws have the same value as any 4 baubles.
4. When the customer bought some of each kind of ornament, he found out exactly one of these salespersons was lying, while the other two told the truth.

Which salesperson was the liar?

If the value of each bauble, gewgaw and trinket were
zero, then all three sales persons would be making
truthful statements, yet it is given that one and
only one salesperson was lying.

In order to deduce which salesperson is lying, an assumption
is made that each of bauble, trinket and gewgaw are assigned positive values.
 
If the honest salespeople were the first and second,
then, by substitution,
7 baubles + (4 baubles + 9 trinkets) = 6 trinkets,
which gives: 1 bauble = -3/11 trinkets...a negative value.
Thus an invalid quote by one of the two salespersons.

If the honest salespeople were the first and third,
then, by substitution,
(7 baubles + 5 gewgaws) + 3 gewgaws = 4 baubles
which gives: 1 bauble = -8/3 gewgaws...a negative value.
Thus an invalid quote by one of the two salespersons.

If the honest salespeople were the second and third,
then, by substitution
(6 trinkets + 3 gewgaws) + 9 trinkets = 5 gewgaws
which gives: 1 trinket = 2/15 gewgaws (or 1 gewgaw = 15/2 trinkets), and, again by substitution,
6*(2/15 gewgaws) + 3 gewgaws = 4 baubles
shows 1 bauble = 57/60 gewgaws (or 1 gewgaw = 60/57 baubles), demonstrating positive values for the Outre Ornaments
which leaves the first salesperson as the liar.

Posted by Dej Mar on 2013-03-13 07:49:41