問88
頻出度★★★
9 けたの数字に対して, 次のルールでチェックディジットを最後尾に付けることにした。チェックディジットを付加した 10 けたの数字として, 正しいものはどれか。 ルール 1 : 各けたの数字を合計する。 ルール 2 : ルール 1 で得られた数が 2 けたになった場合には, 得られた数の各けたの数字を合計する。この操作を, 得られた数が 1 けたになるまで繰り返す。 ルール 3 : 最終的に得られた 1 けたの数をチェックディジットとする。
平成22年度 秋期 ITパスポート試験 問88
テクノロジ系データベース › データベース設計
This question's explanation and your answers so far.
解説
問 88
Incorrectア
The first 9 digits are 123456789, and the sum is 1+2+3+4+5+6+7+8+9=45. Since it has 2 digits, 4+5=9, so the check digit must be 9. However, the last digit is 0, so this is not a 10-digit number with a correctly appended check digit. Corrected, it would be 1234567899.
Incorrectイ
The first 9 digits are 444444444, and the sum is 4×9=36. Since it has 2 digits, 3+6=9, so the correct check digit is 9. However, the last digit is 4, so it does not match. Because the same digit repeats throughout, it looks plausible at first glance, but it does not hold up when you calculate it according to the rules.
Incorrectウ
The first 9 digits are 554433221, and the sum is 5+5+4+4+3+3+2+2+1=29. Since it has 2 digits, 2+9=11, which still has 2 digits, so 1+1=2, meaning the correct check digit is 2. However, the last digit is 1, so it does not match. This is an easy wrong choice to pick if you stop after applying Rule 2 only once and treat 11 as the result, or if you make a mistake partway through the calculation.
- エ
正解 The correct answer is エ. The rule is: sum the digits of the first 9 digits; if the result has 2 digits, sum its digits again, repeating until a single digit remains; then append that single digit at the very end as the check digit. So a 10-digit number is correct when the value computed from its first 9 digits matches its last digit. The first 9 digits of エ are 665533333, and 6+6+5+5+3+3+3+3+3=37 (Rule 1). Since 37 has 2 digits, 3+7=10, and 10 still has 2 digits, so 1+0=1 (Rule 2 repeated twice). The final single digit is 1 (Rule 3), which matches exactly the last digit 1 of エ. Therefore エ is the correct 10-digit number. Note that the value found here is the same as the remainder when the sum of the digits is divided by 9 (using 9 when the remainder is 0), and with this idea you can check the answer quickly without adding up all the digits again.
ここがポイント
- A check digit is a digit computed by a predetermined formula and appended to the end of a code so that input errors or reading errors in the code can be detected. As in this question, an error is detected by checking whether the value computed from the higher-order digits matches the actual last digit.
- The key point of Rule 2 is that you repeat it until the result becomes a single digit. Do not stop at 29 → 11; go on to 11 → 2. Do not stop at 37 → 10; go on to 10 → 1. The result equals the remainder when the sum of the digits is divided by 9 (using 9 when the remainder is 0), so it can be used to check your work.
用語