Proof. Find 2⁄3 of 1⁄3 , of 315.
| 1 | 315 | |
| 2⁄3 | 210 | |
| 1⁄3 | 105 | |
| 2⁄3 of 1⁄3 | 70 |
These are those that he brought.
This problem indicates the method by which, when the herdsman brings to the owner or his accountant his tribute of cattle, the total count of the herd can be determined.
In the papyrus the author wrote, "Example of reckoning tribute," and though the tribute, 70 cattle, is then given, the conversation between the accountant and the herdsman implies that this is to be calculated from the number of the entire herd. But the calculations given are a solution of the inverse problem, to find the entire herd from the number of tribute-cattle, and only at the end, as a proof of these calculations, is the number of tribute-cattle determined from the number of the entire herd.
The problem is very similar to Problems 35-38, and the method of solution is the same as the method used in those problems. See Introduction, page 28.
Problem 66
Suppose a scribe says to thee, Four overseers have drawn 100 great quadruple hekat of grain, their gangs consisting, respectively, of 12, 8, 6 and 4 men. How much does each overseer receive?
There are 30 men in all. Multiply 30 so as to get 100; it makes 31⁄3 The amount given for each man is therefore 31⁄41⁄161⁄64' hekat 12⁄3, ro, Take this amount 12 times for the first overseer, 8 times for the second. 6 times for the third, and 4 times for the fourth.
The multiplication.
| 1 | 31⁄41⁄161⁄64 | hekat | 12⁄3 | ro | |
| 2 | 61⁄21⁄81⁄32 | " | 31⁄3 | " | |
| 4 | 131⁄41⁄161⁄64 | " | 12⁄3 | " | |
| 8 | 261⁄21⁄81⁄32 | " | 31⁄3 | " |
List of the amounts of grain for the four overseers:
The first with 12 workmen will have
1⁄4 of 100 hekat 15 hekat or 40 hekat
The second with 8 workmen will have
1⁄4 of 100 hekat 1 1⁄21⁄81⁄32 hekat 31⁄3ro " 262⁄3 "
The third with 6 workmen will have
20 hekat " 20 "
