The answers to today’s puzzles
Let A equal the price of pens, B equal the price of erasers, and C equal the price of pencils.Combining Robbie and Gary’s statements, we get 11A=−3C. This is impossible.Combining Jason and Robbie’s statements, we get 8B=−3A. This is impossible.
Either Robbie is lying, which means that Gary and Jason are telling the truth. . Or Robbie is not lying, which means that Gary must be lying and Jason must also be lying But since there can be only one liar, we can eliminate this scenario, and thus Robbie is the liar.people are in a room. Everyone is wearing either an orange or an indigo birthday hat. Each person can see the other people’s hats but not their own.
One of them shouts, “If you can see at least 6 orange hats and at least 6 indigo hats, raise your glass!”We know that there are at least 6 people with orange hats and 6 people with indigo hats. But since no one can see their own hats, there must be more people. If there are 7+ people with an orange hat and 7+ people with an indigo hat, then there are 14+ people who would raise their glasses - more than the actual 12. Therefore there must be 6 people with a hat of one colour , and more than 6 with a hat of the other colour .
The people with an orange hat can see only 5 other orange hats, so they don’t raise their glasses. But all people with an indigo hat will raise their glasses. Therefore there are 12 people with indigo hats. Add the 6 with an orange hat, and we get a total of 18.I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one,
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