Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 3.9 AMC 10/12 Find the answer South Africa

The digits from $1$ to $9$ are added, in order, over and over again until the total is $460$ .

$1+2+3+4+5+6+7+8+9+1+2+3+\ldots$

The last digit that was added is

Pick one

Solution

The digits $1$ to $9$ total $45$ , and $460 = 10 \times 45 + 10$ . So the complete set $1\ldots9$ will appear ten times, and then as many more digits as total $10$ , viz. $1+2+3+4$ . So the last digit is $4$ .

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