Eight friends decided to try white-water rafting on a nearby river. They rented four two-person rafts; one was yellow, one was green, one was red, and one was blue. They selected partners for the four rafts and agreed on a destination at the end of a white-water run.
1. Phil and Cook, who were in the same raft, arrived at the destination without incident, but they were not the ones who finished first. 2. The red raft capsized and did not finish; the green raft was first to finish the white-water run. 3. O’Brien and LeRoy were not on the same raft. 4. Paul and Wilson finished last on their raft. 5. Fortunately, Henry is a good swimmer, and he helped his partner, Hughes (whose first name is not Walt), get to shore. They were able to recover their capsized raft, but declined to finish the white-water run. 6. Frank was the first to select a raft, and he picked the yellow one. He and Hawley were on the second raft to finish the white-water run. 7. Alan and Hughes were on the same raft; they were the first to finish the whitewater run. 8. LeRoy and Smith completed the run and were not in last place. 9. After their nearly tragic capsizing experience, Don and his partner, Gladstone, vowed not to set foot in another raft. 10. Alan did not care that he and his partner finished last; he was just glad they made it.

(a) Based on the following statements, one of which is false, what is the first name (Alan, Don, Frank, Henry, LeRoy, Paul, Phil, or Walt) and surname (Cook, Gladstone, Hawley, Huges, O’Brien, Sands, Smith, or Wilson) of each of the friends? (b) Which were partners on the four rafts? (c) What color raft was used by each?

We note that statements 7 (Alan is first) and 10 (Alan did not finish) are contradictory, so one of them must be false. Statement 5 has Henry & Hughes together, so is not consistent with statement 7 (Alan & Hughes). So, statement 7 is inconsistent with two other statements, thus must be the false one.

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The attached table shows how we parsed the statements. An "O" signifies a combination that must occur; and "X" signifies one that cannot occur. We have used "-" to fill the spaces that are inconsistent with the locations of "O". The red letters are deduced from the others.

The first complete set we found was Henry & Hughes (Don & Gladstone) who were in the (red) capsized raft and did not finish. The second complete set we found was Phil & Cook (Frank & Hawley) who were in the (yellow) raft that finished second. We know Paul & Wilson (Alan & Partner) finished last, so Phil & Cook could not have been Paul and Wilson. Finally, O'Brien and Leroy were not on the same boat, so Paul must be Paul O'Brien and Leroy must be Leroy Sands.