UPC barcodes are comprised of 59 alternating bars and gaps (30 bars, 29 gaps). Each of these bars or gaps has a particular relative width. A bar 2 units wide, for example, is twice as thick as a gap 1 unit wide. Each digit is composed of four consecutive bars and gaps, each a total of seven units wide. Widths for each of the digits are given below:
0 = 3-2-1-1
1 = 2-2-2-1
2 = 2-1-2-2
3 = 1-4-1-1
4 = 1-1-3-2
5 = 1-2-3-1
6 = 1-1-1-4
7 = 1-3-1-2
8 = 1-2-1-3
9 = 3-1-1-2
In addition, every barcode has fixed calibration codes at the start (1-1-1), middle (1-1-1-1-1), and end (1-1-1). The full encoding of a UPC-A barcode is:
- Start code (bar-space-bar)
- 6 digits (each space-bar-space-bar)
- Middle code (space-bar-space-bar-space)
- 6 digits (each bar-space-bar-space)
- End code (bar-space-bar)
The five UPC codes given then decode as follows:
Widths: 1-1-1 2-2-2-1 1-4-1-1 2-2-2-1 1-2-3-1 3-2-1-1 1-1-3-2 1-1-1-1-1 3-2-1-1 3-2-1-1 2-1-2-2 1-1-1-4 3-2-1-1 3-2-1-1 1-1-1
Digits: 131504 002600
Widths: 1-1-1 2-1-2-2 2-2-2-1 2-2-2-1 3-1-1-2 3-2-1-1 3-2-1-1 1-1-1-1-1 2-2-2-1 1-2-1-3 3-2-1-1 1-2-3-1 3-2-1-1 2-2-2-1 1-1-1
Digits: 211900 180501
Widths: 1-1-1 2-2-2-1 2-1-2-2 3-2-1-1 3-2-1-1 2-1-2-2 2-2-2-1 1-1-1-1-1 2-2-2-1 1-1-1-4 3-2-1-1 1-4-1-1 3-2-1-1 3-2-1-1 1-1-1
Digits: 120021 160300
Widths: 1-1-1 2-2-2-1 1-1-1-4 3-2-1-1 1-4-1-1 3-2-1-1 3-2-1-1 1-1-1-1-1 2-2-2-1 1-4-1-1 3-2-1-1 3-1-1-2 2-2-2-1 1-1-3-2 1-1-1
Digits: 160300 130914
Widths: 1-1-1 3-2-1-1 1-1-1-4 3-2-1-1 2-2-2-1 2-2-2-1 2-2-2-1 1-1-1-1-1 3-2-1-1 1-2-3-1 3-2-1-1 3-2-1-1 2-1-2-2 2-2-2-1 1-1-1
Digits: 060111 050021
After decoding the digits, one should notice that every other digit is either a "0", "1" or "2". Not coincidentally, there are only 26 letters in the alphabet, and if you assign them numbers 01-26, the first digit is always "0", "1", or "2". Each pair of digits corresponds to a letter, except 00, which represents a space.
| 1st UPC | Digits | 13 | 15 | 04 | 00 | 26 | 00 |
| Letters | M | O | D | Z | |||
| 2nd UPC | Digits | 21 | 19 | 00 | 15 | 05 | 01 |
| Letters | U | S | R | E | A | ||
| 3rd UPC | Digits | 12 | 00 | 21 | 16 | 03 | 00 |
| Letters | L | U | P | C | |||
| 4th UPC | Digits | 16 | 03 | 00 | 13 | 09 | 14 |
| Letters | P | C | M | I | N | ||
| 5th UPC | Digits | 06 | 01 | 11 | 05 | 00 | 21 |
| Letters | F | A | K | E | U |
In the order they're numbered, these letters don't make much sense, but they do look promising. If you rearrange them until they form something coherent, you'll get:
FAKE UPC MINUS REAL UPC MOD Z
Except "MOD Z" doesn't make too much sense. That Z was supposed to stay a number after all:
FAKE UPC MINUS REAL UPC MOD 26
Hmm... they have the "fake UPC" already, but the "real UPC" was cut out by Game Control and is nowhere to be found. Where in the world would you find the real UPC at 6 AM on a Saturday?
That's right, Safeway.
(All of the UPC codes can also be looked up on either http://www.upcdatabase.com/ or Google, but I don't think any of the teams knew that.)
At the local San Rafael Safeway, teams re-enacted Supermarket Sweep to find the UPC codes for these items (except some teams couldn't find the maple brown sugar Nature Valley bars). After getting both UPCs, simply interpret them as huge 12-digit numbers, subtract them, and take the remainder after dividing by 26:
| Fake UPC | Real UPC | Difference | Mod 26 | |
| 1st UPC | 131504002600 | 037000432050 | 94,503,570,550 |
12 |
| 2nd UPC | 211900180501 | 044000037550 | 167,900,142,951 |
21 |
| 3rd UPC | 120021160300 | 087684009659 | 32,337,150,641 |
3 |
| 4th UPC | 160300130914 | 016000265905 | 144,299,865,009 |
1 |
| 5th UPC | 060111050021 | 021130280070 | 38,980,769,951 |
19 |
And of course, why would we ever ask someone to calculate a number mod 26 unless we wanted them to turn the result back into letters again?
The numbers 12-21-3-1-19 correspond to LUCAS.
Calling Cranea's Automated Help-Line with passcode LUCAS gives the next destination (try it!). We had originally planned to send them to George Lucas' Skywalker Ranch just northwest of San Rafael, but time pressure forced us to skip "Clue 8" entirely. We changed the message to direct them to clue 9, at Torpedo Wharf.