471. Someone has twelve pints of wine and wants to give away half of it, but he does not have a six-pint container. He has two containers, one holds 8 pints and the other 5 pints; the question is: how can he pour six pints into the eight-pint container?

## Lebesgue's Problem.
471. Regarding this problem, Arago tells that it decided the fate of Poisson, as, by becoming interested in it, he thereby discovered his vocation and devoted his whole life to mathematics. We have already seen a similar problem (336). This one also has 2 solutions:

| 12 | 8 | 5 |
| ---: | ---: | ---: |
| 12 | 0 | 0 |
| 4 | 8 | 0 |
| 4 | 3 | 5 |
| 9 | 3 | 0 |
| 9 | 0 | 3 |
| 1 | 8 | 3 |
| 1 | 6 | 5 |
| 6 | 6 | 0 |


| 12 | 8 | 5 |
| ---: | ---: | ---: |
| 12 | 0 | 0 |
| 7 | 0 | 5 |
| 0 | 7 | 5 |
| 0 | 8 | 4 |
| 8 | 0 | 4 |
| 8 | 4 | 0 |
| 3 | 4 | 5 |
| 3 | 8 | 1 |
| 11 | 0 | 1 |
| 11 | 1 | 0 |
| 6 | 1 | 5 |
| 6 | 6 | 0 |

For more theoretical details, one can refer to the book by W. Ahrens "Mathematische Spiele".

Lebesgue, V. A., a French mathematician, professor at the Faculty of Sciences in Bordeaux. This problem is taken from his "Exercices d'analyse numérique," dedicated to indeterminate analysis and number theory (1859).