EDCP 442 Presentation by Clementina, Chris and Jumia

                               Loaf Sharing Question

Question: Loaf 100 for man 5,, of the 3 above to man 2 those below. What is the difference of share?

Interpretation: Divide 100 loaves among 5 men in such a way that (1) the shares received are in arithmetical progression; and (2) of the largest shares (“the 3 above”) equals the smallest 2 shares (“toman 2 those below”). What is the arithmetical progression?


  Modern Solution

Following the formula for an arithmetic progression

 = a + (n-1) d, where a=first term

                                           n = number of terms

                                            d= common difference

                                            = nth term

Therefore, the five terms are a, a+d, a+2d, a+3d, a+4d

Ancient Solution: To solve this problem with ancient Egyptian methods, we used the method of false position and Egyptian division.

       


Extension:

 As an extension to the problem, we considered a generalized version of the problem in terms of 4 variables: number of loaves, number of people, and then two more variables from the statement "the sum of the first K terms is equal to (1/m)th of the remaining terms."Here, we provide the general solution for a and d in terms of these variables  











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