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The perfect squares from $1$ through $2500,$ inclusive, are printed in a sequence of digits $1491625\ldots2500.$ How many digits are in the sequence

User Rfoo
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1 Answer

24 votes
24 votes

Final answer:

The sequence contains 16 digits.

Step-by-step explanation:

To find the number of digits in the sequence, we need to determine the range of perfect squares from 1 to 2500. The square root of 2500 is 50, so the sequence includes all the perfect squares from 1 to 50. We can count the number of digits in each perfect square and sum them up to find the total number of digits.

The perfect squares from 1 to 50 are: 1, 4, 9, 16, 25, 36, 49, making a total of 8 squares. Counting the digits in each square, we have:
1 digit: 1, 4, 9
2 digits: 16, 25, 36, 49
That gives us a total of 8 single-digit squares and 4 double-digit squares.
Therefore, the number of digits in the sequence is 8 + (4 * 2) = 16 digits.

User GIA
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