Brain Teasers
Eleven People in a Race
Eleven people participated in a race. Larry, Matt, Nick, Oscar, and Pete each predicted who would finish first, second, third, fourth, and fifth.
Larry predicted that Audrey would finish first, Brenda second, Charlotte third, Dawn fourth, and Edith fifth.
Matt predicted that Fran would finish first, Gertrude second, Heather third, Edith fourth, and Dawn fifth.
Nick predicted that Gertrude would finish first, Charlotte second, Edith third, Isabelle fourth, and Judy fifth.
Oscar predicted that Fran would finish first, Gertrude second, Kate third, Brenda fourth, and Isabelle fifth.
Pete predicted that Gertrude would finish first, Fran second, Edith third, Audrey fourth, and Charlotte fifth.
As it turned out, Larry predicted two people's places correctly, Oscar and Pete each predicted one person's place correctly, and neither Matt nor Nick predicted anyone's place correctly. Nick and Oscar each correctly predicted (but in the wrong place) two people who would come in first to fifth, and the other three each correctly predicted (but in the wrong place) one person who would come in first to fifth.
Who won?
Larry predicted that Audrey would finish first, Brenda second, Charlotte third, Dawn fourth, and Edith fifth.
Matt predicted that Fran would finish first, Gertrude second, Heather third, Edith fourth, and Dawn fifth.
Nick predicted that Gertrude would finish first, Charlotte second, Edith third, Isabelle fourth, and Judy fifth.
Oscar predicted that Fran would finish first, Gertrude second, Kate third, Brenda fourth, and Isabelle fifth.
Pete predicted that Gertrude would finish first, Fran second, Edith third, Audrey fourth, and Charlotte fifth.
As it turned out, Larry predicted two people's places correctly, Oscar and Pete each predicted one person's place correctly, and neither Matt nor Nick predicted anyone's place correctly. Nick and Oscar each correctly predicted (but in the wrong place) two people who would come in first to fifth, and the other three each correctly predicted (but in the wrong place) one person who would come in first to fifth.
Who won?
Answer
Isabelle won.Larry and Oscar each correctly predicted three people who would come in first to fifth. This makes six people altogether, but since there could only be five, there must be some overlap. The only one they both predicted was Brenda, so she, the other two correctly predicted by Larry, and the other two correctly predicted by Oscar must have been the five winners. Neither Heather or Judy could have been a winner.
Suppose Dawn finished first to fifth. Since Matt only correctly predicted one person who would come first to fifth, none of Edith, Fran, or Gertrude could have finished first to fifth. Since Pete correctly predicted two people, Audrey and Charlotte must have been winners. But Larry correctly predicted four people. So Dawn could not have been a winner.
Since neither Dawn nor Heather finished first to fifth, the one Matt predicted correctly must have been Edith, Fran, or Gertrude. This one would also have been one of Pete's winners. His other winner must have been Audrey or Charlotte. This one plus Brenda make two winners for Larry. His third winner must be Edith.
This means that neither Fran nor Gertrude could have finished first to fifth, and Oscar's three winners must have been Brenda, Isabelle, and Kate. Now that we know that Edith and Isabelle were both winners, we have Nick's two winners, and Charlotte could not have finished first to fifth.
Now we have four winners and six non-winners. This makes ten people altogether. Since there were obviously five winners, the eleventh person, Audrey, must also have finished first to fifth.
Since Nick predicted no one's place correctly, Edith could not have come third, which means that Pete's correct prediction must have been Audrey coming fourth. In turn, this means that Larry's correct predictions must have been Brenda coming second and Edith coming fifth. Since Isabelle could not have come fifth, Oscar's correct prediction must have been Kate coming third, leaving Isabelle in first.
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