Mathematicall recreations. Or a collection of sundrie problemes, extracted out of the ancient and moderne philosophers, as secrets in nature, and experiments in arithmeticke, geometrie, cosmographie, horolographie, astronomie, navigation, musicke, opticks, architecture, staticke, machanicks, chimestrie, waterworkes, fireworks, &c. ... Most of which were written first in Greeke and Latine, lately compiled in French, by Henry Van Etten Gent. And now delivered in the English tongue, with the examinations, corrections, and augmentations.

3. Three men bought a quantitie of wine, each paid alike, and each was to have alike; it happe∣ned at the last partition that there was 21 Bar∣rells, of which 7 were full, 7 halfe full, and 7 empty, how must they share the wine and vessells, that each have as many vessells one as ano∣ther, & as much wine one as another.

THis may be answered two wayes as follow∣eth, and these numbers 2, 2, 3; or 3, 3, 1, may serve for direction, and signifies that the first person ought to have 3 Barrells full, & as many empty ones, and one which is halfe full; so hee shall have 7 vessells and 3 Barrels, and a halfe of liquor: and one of the other shall in like manner have as much, so there will re∣maine for the third man 1 Barrell full, 5 which are halfe full, and 1 empty, and so every one shall have alike both in vessells and wine. And generally to answere such questions, divide the number of vessells by the number of persons, and if the Quotient be not an intire number, the question is impossible; but when it is an intire number, there must be made as many parts as there are 3 persons, seeing that each part is lesse than the halfe of the said Quotient: as di∣viding 21 by 3 there comes 7 for the Quotient, which may be parted in these thre parts, 2, 2, 3, or 3, 3, 1, each of which being lesse than halfe of 7.