lberries08
25.04.2021 •
Mathematics
Express 40 mm to 12 cm
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Ответ:
There are at most 4 distinct absolute values of elements taken from this sequence. (If there were at least 5 distinct absolute values, then you could pick
each with different absolute values, but that would contradict the given statement "for every five indices ... at least two of ... have the same absolute value".)
The pigeonhole principle then says that 2 of any 5 numbers taken from this sequence have the same absolute value. Both |x| = x and |-x| = x, so there can be at most 8 distinct numbers in the sequence.