Home > Problem of the Week > Archive List > Detail

<< Prev 9/14/2008 Next >>

But Wait Until the Lawyers Get Involved....

A 50-mile-wide oil slick has been discovered off the Pacific Coast. The Environmental Protection Agency (EPA) has proof that four oil tankers were in the area at the time of the 8-million-gallon oil spill. The four corporations that own the tankers have issued the following public statements:

General Oil

  1. We are not responsible for the Pacific oil spill.
  2. Our ship arrived in the area only after Sunshine's was already there.
  3. The Humility Oil tanker arrived after our ship was there.
Sunshine Oil
  1. We are not responsible for the Pacific oil spill.
  2. Our ship arrived in the area only after Genral's was already there.
  3. The last to arrive in the area was Humility Oil's tanker.
Honesty Oil
  1. We are not responsible for the Pacific oil spill.
  2. Both General and Sunshine are lying at least once.
  3. When our ship came to the area, Humility Oil's tanker was already there.
Humility Oil
  1. We are not responsible for the Pacific oil spill.
  2. Our ship arrived in the oil-spill area last.
  3. Our radio-log shows that the Sunshine Oil tanker was the first ship to arrive in the area.
The EPA commissioners determined that of the four oil companies, only one has told the complete truth: the one whose tanker was last to arrive in the oil-spill area. The other companies told the truth only twice in each case, lying once.

Which of the oil companies is guilty of the oil spill?

 

Source: Modern Day Almanac, 1981, p. 44


Hint: The answer is not all of them at some time or other!

Start by making an assumption, such as oil company XYZ is the guilty bcompany....or perhaps the company telling the truth all three times....and see what happens logically.

 


Solution Commentary: The problem's source provides this commentary: If G(3) and S(3) are false, then G(1), G(2), S(1), S(2) must be true. But G(2) and S(2) cannot both be true. Hence G(3) and S(3) are true. Therefore HU(2) is true by S(3).

HO(3) is false; so HO(1) and HO(2) are true, but irrelevant. G(2) is true by HU(3). Thus, since G(3) is also true, and because G cannot have 3 true statements, G(1) is false and General Oil is Guilty!

Are there other ways to reason this out...some perhaps easier?