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For this challenge, you are presented with a set of 11 suspect coins. Of these, it is known that the number of counterfeit coins is either 0, 1 or 2. Each of the counterfeit coins, if any, is known to have come from one of two batches of coins, one of which is too light and the other of which is too heavy. It is also known that a light coin and a heavy coin, taken together, weigh exactly the same as two normal coins. You must identify the counterfeit coins, if any, after 5 weighings or less.

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CaptainEd Mentor

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My solution is very heavy handed. I would consider this totally ugly except that Newbie has managed to find this bizarre way to come up with exactly 3^5 cases, so that a balance scale can divide into three cases. I've got to imagine pcDixie is Very Deep.

I'm certain pcDixie is Much Deeper Than I, because I can neither fathom how you could come up with the exact conditions that result in 3^5 cases, nor intuit the weighings I came up with.

But, enough about me...

Number the coins 123456789AB

A Weighing consists of putting some coins in the Left pan and some other coins in the Right pan, and the Result is H (Left pan is Heavy), L (Left pan is Light) or x (pans balance).Please record the results of the first three weighings:

1) 123x456

2) 147x258

3) 369x78A

You will have three letters, such as HHL, or xLx. Order matters, so HHL is not the same as HLH.

Now, look at the enclosed chart (243 entries, sorry), which tells the two remaining weighings for your cohort of 9 cases.

You'll find your weighing results in columns R1, R2, and R3. The cohort is sorted, so all 9 cases are together.

The two remaining weighings will separate out your 9 cases into HH, HL, Hx, LH, LL, Lx, xH, xL, xx. You can read which coins are bad in the leftmost column.

In the leftmost column, the coins are listed in order, showing their weights. For example, the first row is HxxxxxxLxxx. This means this case involves a Heavy coin 1 and a Light coin 8.

If you question the coverage (are all 243 cases really there?) you're welcome to import this chart into Excel and sort the first column. You'll see that there are no duplicates, and you'll see that each one has 0, 1, or 2 instances of the letters L and/or H.

Coins W1 R1 W2 R2 W3 R3 W4 R4 W5 R5

HxxxxxxLxxx 123x456 H 147x258 H 369x78A H 15x38 H 23x89 H

HxxxxxxxHxx 123x456 H 147x258 H 369x78A H 15x38 H 23x89 L

HxxxxxxxxLx 123x456 H 147x258 H 369x78A H 15x38 H 23x89 x

xxxxLxxxxLx 123x456 H 147x258 H 369x78A H 15x38 L 24x9A H

xxxxLxxxHxx 123x456 H 147x258 H 369x78A H 15x38 L 24x9A L

xxHxLxxxxxx 123x456 H 147x258 H 369x78A H 15x38 L 24x9A x

xxxxLxxLxxx 123x456 H 147x258 H 369x78A H 15x38 x 24x38 H

HxHxxxxxxxx 123x456 H 147x258 H 369x78A H 15x38 x 24x38 L

xxHxxxxLxxx 123x456 H 147x258 H 369x78A H 15x38 x 24x38 x

HxxxxxxxLxx 123x456 H 147x258 H 369x78A L 15x67 H 78x9A H

HxxxxxxxxHx 123x456 H 147x258 H 369x78A L 15x67 H 78x9A L

HxxxxLxxxxx 123x456 H 147x258 H 369x78A L 15x67 H 78x9A x

xxxxLxxxLxx 123x456 H 147x258 H 369x78A L 15x67 L 68x9A H

xxxxLxxxxHx 123x456 H 147x258 H 369x78A L 15x67 L 68x9A L

xxxxLxHxxxx 123x456 H 147x258 H 369x78A L 15x67 L 68x9A x

HxxxxxHxxxx 123x456 H 147x258 H 369x78A L 15x67 x 67x89 H

xxxxLLxxxxx 123x456 H 147x258 H 369x78A L 15x67 x 67x89 L

xxxxxLHxxxx 123x456 H 147x258 H 369x78A L 15x67 x 67x89 x

HxxxxxxxxxL 123x456 H 147x258 H 369x78A x 15x9A H AxB H

HxxxxxxxxxH 123x456 H 147x258 H 369x78A x 15x9A H AxB L

Hxxxxxxxxxx 123x456 H 147x258 H 369x78A x 15x9A H AxB x

xxxxLxxxxxL 123x456 H 147x258 H 369x78A x 15x9A L AxB H

xxxxLxxxxxH 123x456 H 147x258 H 369x78A x 15x9A L AxB L

xxxxLxxxxxx 123x456 H 147x258 H 369x78A x 15x9A L AxB x

xxHxxxHxxxx 123x456 H 147x258 H 369x78A x 15x9A x 78x9A H

xxxxxLxLxxx 123x456 H 147x258 H 369x78A x 15x9A x 78x9A L

HxxxLxxxxxx 123x456 H 147x258 H 369x78A x 15x9A x 78x9A x

xHxxxxxxxLx 123x456 H 147x258 L 369x78A H 24x37 H 7xA H

xHxxxxLxxxx 123x456 H 147x258 L 369x78A H 24x37 H 7xA L

xHxxxxxxHxx 123x456 H 147x258 L 369x78A H 24x37 H 7xA x

xxHLxxxxxxx 123x456 H 147x258 L 369x78A H 24x37 L 3x9 H

xxxLxxxxHxx 123x456 H 147x258 L 369x78A H 24x37 L 3x9 L

xxxLxxxxxLx 123x456 H 147x258 L 369x78A H 24x37 L 3x9 x

xxxLxxLxxxx 123x456 H 147x258 L 369x78A H 24x37 x 15x24 H

xHHxxxxxxxx 123x456 H 147x258 L 369x78A H 24x37 x 15x24 L

xxHxxxLxxxx 123x456 H 147x258 L 369x78A H 24x37 x 15x24 x

xHxxxxxxLxx 123x456 H 147x258 L 369x78A L 24x68 H 6x9 H

xHxxxLxxxxx 123x456 H 147x258 L 369x78A L 24x68 H 6x9 L

xHxxxxxxxHx 123x456 H 147x258 L 369x78A L 24x68 H 6x9 x

xxxLxxxHxxx 123x456 H 147x258 L 369x78A L 24x68 L 8xA H

xxxLxxxxxHx 123x456 H 147x258 L 369x78A L 24x68 L 8xA L

xxxLxxxxLxx 123x456 H 147x258 L 369x78A L 24x68 L 8xA x

xxxLxLxxxxx 123x456 H 147x258 L 369x78A L 24x68 x 13x24 H

xHxxxxxHxxx 123x456 H 147x258 L 369x78A L 24x68 x 13x24 L

xxxxxLxHxxx 123x456 H 147x258 L 369x78A L 24x68 x 13x24 x

xHxxxxxxxxL 123x456 H 147x258 L 369x78A x 24x59 H AxB H

xHxxxxxxxxH 123x456 H 147x258 L 369x78A x 24x59 H AxB L

xHxxxxxxxxx 123x456 H 147x258 L 369x78A x 24x59 H AxB x

xxxLxxxxxxL 123x456 H 147x258 L 369x78A x 24x59 L AxB H

xxxLxxxxxxH 123x456 H 147x258 L 369x78A x 24x59 L AxB L

xxxLxxxxxxx 123x456 H 147x258 L 369x78A x 24x59 L AxB x

xHxLxxxxxxx 123x456 H 147x258 L 369x78A x 24x59 x 2x3 H

xxHxxxxHxxx 123x456 H 147x258 L 369x78A x 24x59 x 2x3 L

xxxxxLLxxxx 123x456 H 147x258 L 369x78A x 24x59 x 2x3 x

xxHxxxxxxxL 123x456 H 147x258 x 369x78A H 378x59B H AxB H

xxHxxxxxxLx 123x456 H 147x258 x 369x78A H 378x59B H AxB L

xxHxxxxxxxx 123x456 H 147x258 x 369x78A H 378x59B H AxB x

HxxxxxLxxxx 123x456 H 147x258 x 369x78A H 378x59B L 1x2 H

xHxxxxxLxxx 123x456 H 147x258 x 369x78A H 378x59B L 1x2 L

xxxLxxxLxxx 123x456 H 147x258 x 369x78A H 378x59B L 1x2 x

xxHxxxxxHxx 123x456 H 147x258 x 369x78A H 378x59B x 9xB H

xxHxxxxxxxH 123x456 H 147x258 x 369x78A H 378x59B x 9xB L

xxxxLxLxxxx 123x456 H 147x258 x 369x78A H 378x59B x 9xB x

xxxxLxxHxxx 123x456 H 147x258 x 369x78A L 678x19B H 4x5 H

xxxLxxHxxxx 123x456 H 147x258 x 369x78A L 678x19B H 4x5 L

xHxxxxHxxxx 123x456 H 147x258 x 369x78A L 678x19B H 4x5 x

xxxxxLxxxHx 123x456 H 147x258 x 369x78A L 678x19B L AxB H

xxxxxLxxxxH 123x456 H 147x258 x 369x78A L 678x19B L AxB L

xxxxxLxxxxx 123x456 H 147x258 x 369x78A L 678x19B L AxB x

xxxxxLxxLxx 123x456 H 147x258 x 369x78A L 678x19B x 9xA L

HxxxxxxHxxx 123x456 H 147x258 x 369x78A L 678x19B x 9xA x

xxxxxLxxxxL 123x456 H 147x258 x 369x78A L 678x19B x 9xA x

xHxxLxxxxxx 123x456 H 147x258 x 369x78A x 126x78B H 4x5 H

HxxLxxxxxxx 123x456 H 147x258 x 369x78A x 126x78B H 4x5 L

HHxxxxxxxxx 123x456 H 147x258 x 369x78A x 126x78B H 4x5 x

xxxxxLxxxLx 123x456 H 147x258 x 369x78A x 126x78B L 12x9A H

xxxxxLxxHxx 123x456 H 147x258 x 369x78A x 126x78B L 12x9A L

xxHxxLxxxxx 123x456 H 147x258 x 369x78A x 126x78B L 12x9A x

xxHxxxxxLxx 123x456 H 147x258 x 369x78A x 126x78B x 12x9A H

xxHxxxxxxHx 123x456 H 147x258 x 369x78A x 126x78B x 12x9A L

xxxLLxxxxxx 123x456 H 147x258 x 369x78A x 126x78B x 12x9A x

xxxHxxxxxLx 123x456 L 147x258 H 369x78A H 24x68 H 8xA H

xxxHxxxLxxx 123x456 L 147x258 H 369x78A H 24x68 H 8xA L

xxxHxxxxHxx 123x456 L 147x258 H 369x78A H 24x68 H 8xA x

xLxxxHxxxxx 123x456 L 147x258 H 369x78A H 24x68 L 6x9 H

xLxxxxxxHxx 123x456 L 147x258 H 369x78A H 24x68 L 6x9 L

xLxxxxxxxLx 123x456 L 147x258 H 369x78A H 24x68 L 6x9 x

xLxxxxxLxxx 123x456 L 147x258 H 369x78A H 24x68 x 13x24 H

xxxHxHxxxxx 123x456 L 147x258 H 369x78A H 24x68 x 13x24 L

xxxxxHxLxxx 123x456 L 147x258 H 369x78A H 24x68 x 13x24 x

xxxHxxxxLxx 123x456 L 147x258 H 369x78A L 24x37 H 3x9 H

xxLHxxxxxxx 123x456 L 147x258 H 369x78A L 24x37 H 3x9 L

xxxHxxxxxHx 123x456 L 147x258 H 369x78A L 24x37 H 3x9 x

xLxxxxHxxxx 123x456 L 147x258 H 369x78A L 24x37 L 7xA H

xLxxxxxxxHx 123x456 L 147x258 H 369x78A L 24x37 L 7xA L

xLxxxxxxLxx 123x456 L 147x258 H 369x78A L 24x37 L 7xA x

xLLxxxxxxxx 123x456 L 147x258 H 369x78A L 24x37 x 15x24 H

xxxHxxHxxxx 123x456 L 147x258 H 369x78A L 24x37 x 15x24 L

xxLxxxHxxxx 123x456 L 147x258 H 369x78A L 24x37 x 15x24 x

xxxHxxxxxxL 123x456 L 147x258 H 369x78A x 24x59 H AxB H

xxxHxxxxxxH 123x456 L 147x258 H 369x78A x 24x59 H AxB L

xxxHxxxxxxx 123x456 L 147x258 H 369x78A x 24x59 H AxB x

xLxxxxxxxxL 123x456 L 147x258 H 369x78A x 24x59 L AxB H

xLxxxxxxxxH 123x456 L 147x258 H 369x78A x 24x59 L AxB L

xLxxxxxxxxx 123x456 L 147x258 H 369x78A x 24x59 L AxB x

xxLxxxxLxxx 123x456 L 147x258 H 369x78A x 24x59 x 2x3 H

xLxHxxxxxxx 123x456 L 147x258 H 369x78A x 24x59 x 2x3 L

xxxxxHHxxxx 123x456 L 147x258 H 369x78A x 24x59 x 2x3 x

xxxxHxxxxLx 123x456 L 147x258 L 369x78A H 15x67 H 23x9A H

xxxxHxxxHxx 123x456 L 147x258 L 369x78A H 15x67 H 23x9A L

xxxxHxLxxxx 123x456 L 147x258 L 369x78A H 15x67 H 23x9A x

LxxxxxxxxLx 123x456 L 147x258 L 369x78A H 15x67 L 23x9A H

LxxxxxxxHxx 123x456 L 147x258 L 369x78A H 15x67 L 23x9A L

LxxxxHxxxxx 123x456 L 147x258 L 369x78A H 15x67 L 23x9A x

xxxxHHxxxxx 123x456 L 147x258 L 369x78A H 15x67 x 15x24 H

LxxxxxLxxxx 123x456 L 147x258 L 369x78A H 15x67 x 15x24 L

xxxxxHLxxxx 123x456 L 147x258 L 369x78A H 15x67 x 15x24 x

xxxxHxxxLxx 123x456 L 147x258 L 369x78A L 15x38 H 3x9 H

xxLxHxxxxxx 123x456 L 147x258 L 369x78A L 15x38 H 3x9 L

xxxxHxxxxHx 123x456 L 147x258 L 369x78A L 15x38 H 3x9 x

LxxxxxxHxxx 123x456 L 147x258 L 369x78A L 15x38 L 8xA H

LxxxxxxxxHx 123x456 L 147x258 L 369x78A L 15x38 L 8xA L

LxxxxxxxLxx 123x456 L 147x258 L 369x78A L 15x38 L 8xA x

xxxxHxxHxxx 123x456 L 147x258 L 369x78A L 15x38 x 15x24 H

LxLxxxxxxxx 123x456 L 147x258 L 369x78A L 15x38 x 15x24 L

xxLxxxxHxxx 123x456 L 147x258 L 369x78A L 15x38 x 15x24 x

xxxxHxxxxxL 123x456 L 147x258 L 369x78A x 15x24 H 2xB H

xxxxHxxxxxH 123x456 L 147x258 L 369x78A x 15x24 H 2xB L

xxxxHxxxxxx 123x456 L 147x258 L 369x78A x 15x24 H 2xB x

LxxxxxxxxxL 123x456 L 147x258 L 369x78A x 15x24 L 2xB H

LxxxxxxxxxH 123x456 L 147x258 L 369x78A x 15x24 L 2xB L

Lxxxxxxxxxx 123x456 L 147x258 L 369x78A x 15x24 L 2xB x

LxxxHxxxxxx 123x456 L 147x258 L 369x78A x 15x24 x 5x6 H

xxxxxHxHxxx 123x456 L 147x258 L 369x78A x 15x24 x 5x6 L

xxLxxxLxxxx 123x456 L 147x258 L 369x78A x 15x24 x 5x6 x

xxxxxHxxxxL 123x456 L 147x258 x 369x78A H 678x19B H AxB H

xxxxxHxxxLx 123x456 L 147x258 x 369x78A H 678x19B H AxB L

xxxxxHxxxxx 123x456 L 147x258 x 369x78A H 678x19B H AxB x

xxxHxxLxxxx 123x456 L 147x258 x 369x78A H 678x19B L 4x5 H

xxxxHxxLxxx 123x456 L 147x258 x 369x78A H 678x19B L 4x5 L

xLxxxxLxxxx 123x456 L 147x258 x 369x78A H 678x19B L 4x5 x

xxxxxHxxHxx 123x456 L 147x258 x 369x78A H 678x19B x 9xB H

xxxxxHxxxxH 123x456 L 147x258 x 369x78A H 678x19B x 9xB L

LxxxxxxLxxx 123x456 L 147x258 x 369x78A H 678x19B x 9xB x

xLxxxxxHxxx 123x456 L 147x258 x 369x78A L 378x59B H 1x2 H

LxxxxxHxxxx 123x456 L 147x258 x 369x78A L 378x59B H 1x2 L

xxxHxxxHxxx 123x456 L 147x258 x 369x78A L 378x59B H 1x2 x

xxLxxxxxxHx 123x456 L 147x258 x 369x78A L 378x59B L AxB H

xxLxxxxxxxH 123x456 L 147x258 x 369x78A L 378x59B L AxB L

xxLxxxxxxxx 123x456 L 147x258 x 369x78A L 378x59B L AxB x

xxLxxxxxLxx 123x456 L 147x258 x 369x78A L 378x59B x 12x9A H

xxLxxxxxxxL 123x456 L 147x258 x 369x78A L 378x59B x 12x9A x

xxxxHxHxxxx 123x456 L 147x258 x 369x78A L 378x59B x 12x9A x

xxxxxHxxLxx 123x456 L 147x258 x 369x78A x 126x78B H 12x9A H

xxxxxHxxxHx 123x456 L 147x258 x 369x78A x 126x78B H 12x9A L

xxLxxHxxxxx 123x456 L 147x258 x 369x78A x 126x78B H 12x9A x

xLxxHxxxxxx 123x456 L 147x258 x 369x78A x 126x78B L 1x2 H

LxxHxxxxxxx 123x456 L 147x258 x 369x78A x 126x78B L 1x2 L

LLxxxxxxxxx 123x456 L 147x258 x 369x78A x 126x78B L 1x2 x

xxLxxxxxxLx 123x456 L 147x258 x 369x78A x 126x78B x 12x9A H

xxLxxxxxHxx 123x456 L 147x258 x 369x78A x 126x78B x 12x9A L

xxxHHxxxxxx 123x456 L 147x258 x 369x78A x 126x78B x 12x9A x

xLHxxxxxxxx 123x456 x 147x258 H 369x78A H 368x1AB H 17x24 H

xxHHxxxxxxx 123x456 x 147x258 H 369x78A H 368x1AB H 17x24 L

xxxxLHxxxxx 123x456 x 147x258 H 369x78A H 368x1AB H 17x24 x

xxxxxxxLHxx 123x456 x 147x258 H 369x78A H 368x1AB L 9xB H

xxxxxxxLxxH 123x456 x 147x258 H 369x78A H 368x1AB L 9xB L

xxxxxxxLxxx 123x456 x 147x258 H 369x78A H 368x1AB L 9xB x

xxxxxxxLxxL 123x456 x 147x258 H 369x78A H 368x1AB x AxB H

xxxxxxxLxLx 123x456 x 147x258 H 369x78A H 368x1AB x AxB L

HxxxxHxxxxx 123x456 x 147x258 H 369x78A H 368x1AB x AxB x

xxxxxxHxxxL 123x456 x 147x258 H 369x78A L 367x2AB H 9xB H

xxxxxxHxLxx 123x456 x 147x258 H 369x78A L 367x2AB H 9xB L

xxxxxxHxxxx 123x456 x 147x258 H 369x78A L 367x2AB H 9xB x

HxLxxxxxxxx 123x456 x 147x258 H 369x78A L 367x2AB L 15x27 H

xxLxLxxxxxx 123x456 x 147x258 H 369x78A L 367x2AB L 15x27 L

xxxHxLxxxxx 123x456 x 147x258 H 369x78A L 367x2AB L 15x27 x

xxxxxxHxxHx 123x456 x 147x258 H 369x78A L 367x2AB x AxB H

xxxxxxHxxxH 123x456 x 147x258 H 369x78A L 367x2AB x AxB L

xLxxxLxxxxx 123x456 x 147x258 H 369x78A L 367x2AB x AxB x

xxxxxxxLLxx 123x456 x 147x258 H 369x78A x 12x78 H 23x9A H

xxxxxxxLxHx 123x456 x 147x258 H 369x78A x 12x78 H 23x9A L

HxxHxxxxxxx 123x456 x 147x258 H 369x78A x 12x78 H 23x9A x

xxxxxxHxxLx 123x456 x 147x258 H 369x78A x 12x78 L 13x9A H

xxxxxxHxHxx 123x456 x 147x258 H 369x78A x 12x78 L 13x9A L

xLxxLxxxxxx 123x456 x 147x258 H 369x78A x 12x78 L 13x9A x

xxxHLxxxxxx 123x456 x 147x258 H 369x78A x 12x78 x 24x36 H

HLxxxxxxxxx 123x456 x 147x258 H 369x78A x 12x78 x 24x36 L

xxxxxxHLxxx 123x456 x 147x258 H 369x78A x 12x78 x 24x36 x

xxHxHxxxxxx 123x456 x 147x258 L 369x78A H 367x2AB H 5x6 H

xxxLxHxxxxx 123x456 x 147x258 L 369x78A H 367x2AB H 5x6 L

LxHxxxxxxxx 123x456 x 147x258 L 369x78A H 367x2AB H 5x6 x

xxxxxxLxHxx 123x456 x 147x258 L 369x78A H 367x2AB L 9xB H

xxxxxxLxxxH 123x456 x 147x258 L 369x78A H 367x2AB L 9xB L

xxxxxxLxxxx 123x456 x 147x258 L 369x78A H 367x2AB L 9xB x

xxxxxxLxxxL 123x456 x 147x258 L 369x78A H 367x2AB x AxB H

xxxxxxLxxLx 123x456 x 147x258 L 369x78A H 367x2AB x AxB L

xHxxxHxxxxx 123x456 x 147x258 L 369x78A H 367x2AB x AxB x

xxxxxxxHxxL 123x456 x 147x258 L 369x78A L 368x1AB H 9xB H

xxxxxxxHLxx 123x456 x 147x258 L 369x78A L 368x1AB H 9xB L

xxxxxxxHxxx 123x456 x 147x258 L 369x78A L 368x1AB H 9xB x

xHLxxxxxxxx 123x456 x 147x258 L 369x78A L 368x1AB L 24x78 H

xxLLxxxxxxx 123x456 x 147x258 L 369x78A L 368x1AB L 24x78 L

xxxxHLxxxxx 123x456 x 147x258 L 369x78A L 368x1AB L 24x78 x

xxxxxxxHxHx 123x456 x 147x258 L 369x78A L 368x1AB x AxB H

xxxxxxxHxxH 123x456 x 147x258 L 369x78A L 368x1AB x AxB L

LxxxxLxxxxx 123x456 x 147x258 L 369x78A L 368x1AB x AxB x

xxxxxxLxLxx 123x456 x 147x258 L 369x78A x 12x78 H 34x9A H

xxxxxxLxxHx 123x456 x 147x258 L 369x78A x 12x78 H 34x9A L

xHxxHxxxxxx 123x456 x 147x258 L 369x78A x 12x78 H 34x9A x

xxxxxxxHxLx 123x456 x 147x258 L 369x78A x 12x78 L 23x9A H

xxxxxxxHHxx 123x456 x 147x258 L 369x78A x 12x78 L 23x9A L

LxxLxxxxxxx 123x456 x 147x258 L 369x78A x 12x78 L 23x9A x

LHxxxxxxxxx 123x456 x 147x258 L 369x78A x 12x78 x 24x36 H

xxxLHxxxxxx 123x456 x 147x258 L 369x78A x 12x78 x 24x36 L

xxxxxxLHxxx 123x456 x 147x258 L 369x78A x 12x78 x 24x36 x

xxxxxxxxxLL 123x456 x 147x258 x 369x78A H 12x9A H 1xB H

xxxxxxxxxLH 123x456 x 147x258 x 369x78A H 12x9A H 1xB L

xxxxxxxxxLx 123x456 x 147x258 x 369x78A H 12x9A H 1xB x

xxxxxxxxHxL 123x456 x 147x258 x 369x78A H 12x9A L 1xB H

xxxxxxxxHxH 123x456 x 147x258 x 369x78A H 12x9A L 1xB L

xxxxxxxxHxx 123x456 x 147x258 x 369x78A H 12x9A L 1xB x

xxxxxxLLxxx 123x456 x 147x258 x 369x78A H 12x9A x 12x37 H

xxHxxHxxxxx 123x456 x 147x258 x 369x78A H 12x9A x 12x37 L

xxxxxxxxHLx 123x456 x 147x258 x 369x78A H 12x9A x 12x37 x

xxxxxxxxLxL 123x456 x 147x258 x 369x78A L 12x9A H 1xB H

xxxxxxxxLxH 123x456 x 147x258 x 369x78A L 12x9A H 1xB L

xxxxxxxxLxx 123x456 x 147x258 x 369x78A L 12x9A H 1xB x

xxxxxxxxxHL 123x456 x 147x258 x 369x78A L 12x9A L 1xB H

xxxxxxxxxHH 123x456 x 147x258 x 369x78A L 12x9A L 1xB L

xxxxxxxxxHx 123x456 x 147x258 x 369x78A L 12x9A L 1xB x

xxLxxLxxxxx 123x456 x 147x258 x 369x78A L 12x9A x 12x37 H

xxxxxxHHxxx 123x456 x 147x258 x 369x78A L 12x9A x 12x37 L

xxxxxxxxLHx 123x456 x 147x258 x 369x78A L 12x9A x 12x37 x

HxxxHxxxxxx 123x456 x 147x258 x 369x78A x 129x678 H 1x2 H

xHxHxxxxxxx 123x456 x 147x258 x 369x78A x 129x678 H 1x2 L

xxxxxxxxHHx 123x456 x 147x258 x 369x78A x 129x678 H 1x2 x

xLxLxxxxxxx 123x456 x 147x258 x 369x78A x 129x678 L 1x2 H

LxxxLxxxxxx 123x456 x 147x258 x 369x78A x 129x678 L 1x2 L

xxxxxxxxLLx 123x456 x 147x258 x 369x78A x 129x678 L 1x2 x

xxxxxxxxxxL 123x456 x 147x258 x 369x78A x 129x678 x 1xB H

xxxxxxxxxxH 123x456 x 147x258 x 369x78A x 129x678 x 1xB L

xxxxxxxxxxx 123x456 x 147x258 x 369x78A x 129x678 x 1xB x

Actually, pcDixie, I'm sorry to sound like I'm griping--I'm totally amazed at your ability to discover (or invent) that problem, and I greatly enjoyed both considering how to construct the first three weighings, and how to make an Excel macro to enable me to see the results of a weighing on a bunch of cases.

So, thanks so very much! (I just wish I understood my answer, grumble...)

Edited by CaptainEd
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