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BT. PLACING OBJECTS IN CONTACT



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6.BT. PLACING OBJECTS IN CONTACT
New section. The objects involved are usually common objects such as coins or cigarettes, etc. The standard recreation is to have them all touching one another. However, the more basic question of how many spheres can touch a sphere goes back to Kepler and perhaps the Greeks. Similar questions have been asked about cubes, etc.
Endless Amusement II. 1826? Problem II, p. 189. "Five shillings or sixpences may be so placed over each other, as to be all visible and all be in contact." Two solutions. The first has two coins on the table, then two coins on top moved far enough onto one of the lower coins that a vertical coin can touch both of them and the two lower coins at once. The second solution has one coin with two coins on top and two slanted coins sitting on the bottom coin and touching both coins in the second layer and then touching each other up in the air. [I have recently read an article analysing this last solution and showing that it doesn't work if the coin is too thick and that the US nickel is too thick.] = New Sphinx, c1840, p. 131.

Will Baffel. Easy Conjuring without apparatus. Routledge & Dutton, nd, 4th ptg [c1910], pp. 103-104. Six matches, each touching all others. Make a V with two matches and place a third match in the notch to make a short arrow. Lie one of these on top of another.

Will Blyth. Money Magic. C. Arthur Pearson, London, 1926. Five in contact, pp. 98-101. Same as Endless Amusement II.

Rohrbough. Puzzle Craft. 1932. Six Nails, p. 22 (= p. 22 of 1940??). As in Baffel.

Meyer. Big Fun Book. 1940. Five coins, p. 543. Same as the first version in Endless Amusement II.

Philip Kaplan. More Posers. (Harper & Row, 1964); Macfadden-Bartell Books, 1965. Prob. 29, pp. 35 & 92. Second of the forms given in Endless Amusement II.

Ripley's Puzzles and Games. 1966. P. 36. Six cigarettes, as in Baffel.

I recall this is in Gardner and that a solution with 6 cigarettes was improved to 7.



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