# Knight Cumulina

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### Puzzle Of The Week

An auditioning call for new cast members at theme park results in a room filled with 25 people, each of them costumed as a knight, a serf, or a damsel. It is agreed that each knight will always tell the truth, each serf will always tell lies, and each damsel will alternate between telling the truth and lying. When each of them is asked in turn, "Are you a knight?", 17 say "Yes". When each of them is asked in turn, "Are you a damsel?", 12 say "Yes". When each of them is asked in turn, "Are you a serf?", 8 say "Yes".

How many knights are in the room?

from *The Ultimate Mathematical Challenge* by The UK Mathematics Trust

*solution below*

### Image Of The Week

The Smithsonian’s National Museum of American History has acquired the taxidermied remains of Cumulina (pictured above), the world’s first successfully cloned mouse, who was created in a laboratory at the University of Hawaii in 1997 and who died in her sleep in 2000 at the advanced age of two years and seven months — the equivalent of 95 in human years. The museum has also acquired a set of Cumulina’s footprints made on her second birthday.

### Puzzle Solution

**Solution:** Five. Suppose there are *k* knights and *s* serfs altogether, and suppose there are *d* damsels who lied to the first question. In answer to the first question, the people who answered *Yes* were the knights (truthfully), the serfs (untruthfully) and the damsels who lied to the first question they were asked. This gives the equation k + s + d = 17. In answer to the second question, the people who answered *Yes* were the serfs (untruthfully) and the damsels who lied to the first question they were asked but who then answered truthfully. This gives the equation s + d = 12. Subtract the second equation from the second to give k = 5. Hence the number of knights in the group is 5.

from *The Ultimate Mathematical Challenge* by The UK Mathematics Trust

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