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how can we put 45 rabbits in 9 cells, so that there are different number of rabbits in each cell and none of the cells is empty?

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You can put one rabbit in cell one. Two rabbits in cell two. Three rabbits in cell three. Four rabbits in cell four. Five rabbits in cell five. Six rabbits in cell six. Seven rabbits in cell seven. Eight rabbits in cell eight. And finally nine rabbits in cell nine.
45 rabbits in 9 cells

45 - 9 = 36
36 - 8 = 28
28 - 7 = 21
21 - 6 = 15
15 - 5 = 10
10 - 4 = 6
6 - 3 = 3
3 - 2 = 1
1 - 1 = 0

Cell 1 can have 9 rabbits
Cell 2 can have 8 rabbits
Cell 3 can have 7 rabbits 
Cell 4 can have 6 rabbits
Cell 5 can have 5 rabbits
Cell 6 can have 4 rabbits
Cell 7 can have 3 rabbits
Cell 8 can have 2 rabbits
Cell 9 can have 1 rabbits
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