Quiz　“DANGO 3 Brothers”
Shinji Kinoshita, MD

Human Welfare Studies 3: 93-105, 2000

The above figure shows 9 DANGOs (Japanese dumplings) and 8 KUSHIs (straight skewers). On each skewer, there are 3 (brothers of) dumplings. Remove 2 out of the 9 dumplings to other positions and skewer these dumplings so as to increase the number of skewers from 8 to 10. On each skewer, there should be 3 dumplings, and there should not be 2 or 4 dumplings. There will be three forms of answers in this quiz, which are shown in the addendum at the end of this book.
   The original form of this quiz was created by Sir Isaac Newton (1642-1727) as follows: (from: Henry E. Duedeney: Amusements in mathematics).

“Plant nine trees so that they shall form ten straight rows with three trees in every row.”
   Newton showed only one form of answer.  In 1999, however, Kinoshita demonstrated three forms of answers for the first time; and proved that there are no answers except for these forms of answers.