# A Logician, three students and three initials

A logician decides to test three students named Rich, Ken and Rob. He said:

I am thinking of the initials of a full name. First, middle and last. On three separate blank cards I have written those initials. Rich gets the initial for the first name, Ken gets the initial for the middle name and Rob gets the initial of the last name.

Then on the board he shows them a table of the three initials. He tells them that the name's initials is one of these 10 choices.

RICH KEN ROB
FIRST INITIAL MIDDLE INITIAL LAST INITIAL
B D W
C D H
C G M
C F W
C J S
E G W
E G S
E J M
N D H
N J M

He asks, "Can you guess the correct combination?"

Rich looks at his card and says, “I cannot logically guess the combination.”

Ken looks at his card and says, "I also cannot guess the combination."

Rob looks at his card and says, "I know the combination!"

Rich says, "OK. So I know the combination also."

Ken after thinking a bit says, "I definitely know the combination but the other two are wrong!"

The logician asks them to write down their guesses and sure enough Ken was right. Explain what must have happened assuming nobody lied. What was the correct combination?

• @GregMartin is there an alternative explanation to generic people name gendered as male? Commented Sep 13, 2022 at 8:42
• @justhalf - there's always alternatives. But that doesn't change that sadly, this seems to me also, the most likely explanation somewhere down the line..... Commented Sep 14, 2022 at 23:42
• @GregMartin Bias towards what? It's not good or bad to appear in a logic puzzle. Commented Sep 15, 2022 at 13:05
• This puzzle is impossible, because the logician had no way of knowing that Rob would mess up, therefore it must be solvable assuming Rich had M, but it is not, because no M’s are eliminated by Rich’s or Ken’s answers. Commented Dec 15, 2022 at 2:57

I think the correct combination is

EJM

If we go through the conversation:

Rich cannot guess it, so it has to have multiple options on the board - so the first initial is not B.

As Ken cannot guess either, it also has to be an initial that appears multiple times - so it is not CFW.

Rob says they can guess the combination. So with BDW and CFW ruled out, the last initial must be unique. So Rob has W and the match is EGW.

So that’s it right?

Well Rich has followed and also believes the answer is EGW - as the combination matches his first initial E.

But Ken has also followed - but is confused as his middle initial is J. He thinks for a second and realises Rob is looking at his initial upside down - his initial is actually an M not a W, and the correct combination is actually EJM!

• OMG. That was not only fast but very well accomplished. Hats off. Commented Sep 12, 2022 at 13:04
• @RogerA thanks! Clever little puzzle, I enjoyed that a lot, the choice of font in the table was what actually lead me to the twist, as I realised they look similar! Commented Sep 12, 2022 at 13:10
• @BeastlyGerbil Given the relevance of the font to the solution of the problem, perhaps the edit that changed it into a table (and made it go back to the default font) should be reversed? Or perhaps there should be both an image and text version for future solvers? Commented Sep 13, 2022 at 14:29
• @fartgeek it doesn't say anywhere that the logician expected them to get the right combination though. The intended correct answer could simply be - 'we cannot logically solve the puzzle'. Afterall, a lot of multiple choice logic tests have the option 'Cannot tell' which could be what the logician was hoping for. The questions not impossible, as it simply asks what happened and what was the correct answer Commented Dec 15, 2022 at 13:47
• @BeastlyGerbil ooooof you’re right. I apologize and retract my argument. Commented Dec 16, 2022 at 1:34