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James Joseph Sylvester: 2 puzzles worth knowing

2 puzzles from James Joseph Sylvester, each explained in a minute and credited to the original work. Free on Savvy.

• With only 5-cent and 7-cent stamps, what's the largest amount you can never make exactly?

  You have an unlimited supply of stamps in two denominations that share no common factor, say 5 cents and 7 cents. You can combine any number of each. Some amounts are impossible to…

  — James Joseph Sylvester, Mathematical Questions with their Solutions

• Scatter dots on a page so no three ever line up perfectly. Is that actually possible?

  Take any finite set of points on a page, as long as they don't all sit on one single straight line. A mathematician asked: must there always exist at least one line that passes thr…

  — James Joseph Sylvester (posed); Tibor Gallai (proved), Mathematical Question 11851

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