This branch of mathematics is the only one, I believe,in which good writers frequently get results entirely erroneous.. . . It may be doubted if there is a singleextensive treatise on probabilities in existencewhich does not contain solutions absolutely indefensible.
— C. S. PEIRCE, in Popular Science Monthly (1878)
1. An average problem for a mathematically inclined reader.
3. (Solution by Roger Frye, after about 110 hours of computation on a Connection Machine in 1987.) 958004 + 2175194 + 4145604 = 4224814 and (therefore) 1916004 + 4350384 + 8291204 = 8449624.
4. (One of the readers of the preliminary manuscript for this book reported that he had found a truly remarkable proof. But unfortunately ...