How many pairs of the following sets of numbers are exactly alike? 278126 278126, 901272 902172, 826482 824682, 004657 004657, 128532 125832, 278917 278971.

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To determine how many pairs of the given sets of numbers are exactly alike, we need to compare each pair systematically. Two sets of numbers are considered exactly alike if they are identical in every digit and order.

Examining the pairs:

1. The pair 278126 and 278126 are exactly alike since they are the same.

2. The pair 901272 and 902172 are not alike; the digits differ in their positions.

3. The pair 826482 and 824682 are also not alike, as the digits have been rearranged.

4. The pair 004657 and 004657 are exactly alike; they match in both digits and order.

5. The pair 128532 and 125832 are not alike; they differ in the arrangement of digits.

6. The pair 278917 and 278971 are not alike; again, the digits are re-arranged.

From this analysis, we found that there are two pairs (278126 with itself, and 004657 with itself) that are exactly alike. Therefore, the correct answer is indeed two pairs, indicating that the response chosen accurately reflects the number of identical pairs found in the list.

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