All thinkers

Frederick Soddy: 2 puzzles worth knowing

2 puzzles from Frederick Soddy, each explained in a minute and credited to the original work. Free on Savvy.

• Ring six spheres around three that all touch each other — will the ring ever close up?

  Start with three spheres, all mutually touching each other, sitting inside (or alongside) one more enclosing sphere. Now pack a chain of smaller spheres into the gap, each one touc…

  — Frederick Soddy, Soddy's hexlet (independently recorded on an 1822 sangaku tablet)

• Three circles touch each other perfectly — how big is the fourth that touches all three?

  Draw three circles of any size so that each one touches the other two, then draw a fourth circle nestled in the gap between them, also touching all three. Given only the sizes of t…

  — Frederick Soddy, restating René Descartes' 1643 theorem, The Kiss Precise

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