Abstract
Anne, Bill, and Cath all have a positive integer on their forehead. They can only see the foreheads of others. One of the numbers is the sum of the other two. All the previous is common knowledge. They now successively make the truthful announcements:
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1.
Anne: “I don’t know my number.”
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2.
Bill: “I don’t know my number.”
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3.
Cath: “I don’t know my number.”
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4.
Anne: “I know my number. It is 50.”
What are the other numbers?
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© 2015 Springer International Publishing Switzerland
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van Ditmarsch, H., Kooi, B. (2015). Who Has the Sum?. In: One Hundred Prisoners and a Light Bulb. Copernicus, Cham. https://doi.org/10.1007/978-3-319-16694-0_6
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DOI: https://doi.org/10.1007/978-3-319-16694-0_6
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Publisher Name: Copernicus, Cham
Print ISBN: 978-3-319-16693-3
Online ISBN: 978-3-319-16694-0
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