In the vase shown above, a necklace of black and white beads is inserted. The number of white balls between each consecutive black ball follows an arithmetic progression.
How many balls in total does the necklace have?
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If we understand the problem of counting the balls inside and outside, we have to:
White balls are: 1 + 2 + 3 + . . . + 9 + 1 0 = 2 1 0 ( 1 0 + 1 ) = 5 5
(The Gaussian formula was used)
Black balls are a total of 1 1 .
Total balls are:
5 5 + 1 1 = 6 6