[Math] There are 81 trees with {1,2,3,….81} apples on them respectively. Distribute among 9 people. Each get equal apples

combinatoricsrecreational-mathematics

It is clear. There are 81 apple trees. 1st tree has 1 apple, 2nd tree has 2 apples, 81st tree has 81 apples. Distribute the "trees" (not apples) among 9 people so everyone gets equal amount of apples. (which is 369). This is how i started. 5th person gets 369 an others are close to that amount. It might be a wrong approach but anyways…

1   2   3   4   5   6   7   8   9
18  17  16  15  14  13  12  11  10
19  20  21  22  23  24  25  26  27
36  35  34  33  32  31  30  29  28
37  38  39  40  41  42  43  44  45
54  53  52  51  50  49  48  47  46
55  56  57  58  59  60  61  62  63
72  71  70  69  68  67  66  65  64
73  74  75  76  77  78  79  80  81
365 366 367 368 369 370 371 372 373 >> sum

Best Answer

Put them in a 9x9 square, from left to right and top to bottom, and take the diagonals !

  1. 1,11,21,31,41,51,61,71,81 = 369
  2. 2,12,22,32,42,52,62,72,73 = 369
  3. 3,13,23,33,43,53,63,64,74
  4. 4,14,24,34,44,54,55,65,75
  5. and so on
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