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The Genuine Barcode (illustration)
FILE No.97Unsolved

The Genuine Barcode

Difficulty ★★★about 8 minTheft CaseCheck digitsCalculation
The last digit of a 13-digit barcode is a check digit. Which of four numbers passes the check?

Case Record

The last digit of a 13-digit barcode is a check digit. It is set by this rule:

  1. Add the digits in odd positions (1st, 3rd, ... 11th) as they are.
  2. Add the digits in even positions (2nd, 4th, ... 12th) multiplied by 3.
  3. Subtract the last digit of the total from 10 (if that gives 10, use 0). That is the 13th digit.

A warehouse has products with fake barcodes mixed in. Of the four numbers below, only one follows the rule.

Your question

Which is it?

Case Files

Evidence

Diagram

First 12 digits: 491234567890ItemCalculationResultOdd positions4+1+3+5+7+929Even positions9+2+4+6+8+029Even x 329 x 387Total29 + 8711613th digit10 - 64 (match)
Diagram

Timeline

  1. Products with fake barcodes are found.

Hints

If you get stuck, open the hints one at a time, in order.

Open hint 1

Split the first 12 digits into odd and even positions.

Open hint 2

The even positions are multiplied by 3.

Open hint 3

Subtract the last digit of the total from 10.

Solve It

Your question

Which is it?

Choose the answer closest to the truth.

Share: I'm solving this

The Truth

4912345678904

The answer is: 4912345678904.

For the first 12 digits, 491234567890: the odd-position digits (4, 1, 3, 5, 7, 9) add up to 29. The even-position digits (9, 2, 4, 6, 8, 0) add up to 29, and 29 x 3 = 87. Total: 29 + 87 = 116. The last digit is 6, and 10 - 6 = 4, matching the 13th digit.

The other numbers do not match (the correct 13th digits would be 4, 3 and 7 respectively).

Compare the 13th digitNumberCorrectActualResult491234567890444Pass490123456789141Fail493777700012737Fail498100200300070Fail
Diagram of the solution

Key Points

  • Odd positions as they are, even positions times 3
  • Take the last digit of the total, subtract from 10
  • Find the number where the calculation matches

Why people get fooled

People treat the last digit as an ordinary digit and do not realise it is a check number.

Similar tricks

  • The follow-the-procedure type
  • The check-each-number type

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