# What is his full name?

A smart man meets three smart persons (Raj, Lisa and Nick) for the very first time. They ask him his name.

He writes 12 full names on a piece of paper and puts it in front of them. He says his full name is one of the 12.

Then he separately writes down his first name on a piece of paper and only gives it to Raj. So the other two don’t get to see it.

He writes down his middle initial on another piece of paper and only gives it to Lisa. Again Nick and Raj don’t see that.

Then he writes down his surname (last name) on a piece of paper and only gives it to Nick. Raj and Lisa don’t see it.

He asks Raj: Do you know my full name?

Raj responds: No I do not. But I know they do not either.

The man looks at Lisa.

Lisa responds: Hmm. I did not know before Raj spoke and I do not know now.

The man looks at Nick.

Nick says: I did not know before, but now I know your full name.

Raj says: Now I know it too.

Lisa says: Me too.

So what is his full name?

Loosely based on a structure of another puzzle to be disclosed after answers are in.

• Is Ken R Armitstead correct, or should it be Ken R Armistead? Jan 2 '18 at 13:45
• Part of the puzzle Lolgast
– DrD
Jan 2 '18 at 13:48

It should be

Logic behind it:

If his first name is Robert or Ken, Nick might know if his last name is Atkinson or Armitstead (note the additional t), which are unique. Thus, in such a case Ray couldn't say for sure that Nick doesn't know. If his first name is Scott, Lisa might know since the middle letter B is unique. Since Lisa still doesn't know it, it can't be Richard R Armistead (since his R is unique among the remaining options). Since Nick now knows, his last name must be unique for the remaining options and must be Armistead, the corresponding name/initial being Ben A.

From my comment on the OP, and the question in a comment on this one, here's an analysis if Ken R Armitstead was called Ken R Armistead instead (that's a lot of steads right there):

Ken is now a possible first name. Thus, the R is not a unique initial, and we can't eliminate it since Lisa can't gain any info from it. Then, we have 2 unique last names left (Johansson and Fleischman). Since Nick knows, it must be one of those and not Armstrong or Armistead. Then, Lisa also knows since their middle letters are distinct. Poor Ray is left unknowing, however, since they are both called Ken (and the knowledge that Lisa and Nick know his name doesn't help either).

• Wow. Will they guess it if "t" was not there? Lolgast?
– DrD
Jan 2 '18 at 14:01
• @DEEM Added my explanation for that scenario. Jan 2 '18 at 14:13
• "If his first name is Robert or Ken, Nick would know" - this isn't quite right, because it could be Robert P Fleischman or Ken A Johansson. The point is that Nick MIGHT know, so Raj can't say for sure that Nick doesn't know. (I already upvoted though - you got there first :-) ) Jan 2 '18 at 14:17
• Good Explaining. You must be an engineer!
– DrD
Jan 2 '18 at 14:17
• @Randal'Thor Err, yes, that's what I meant as well. I'll edit it so it's clear :P Thanks for the upvote! Jan 2 '18 at 14:21

## Data

Among the names listed, there are:

• 3 Ken, 2 Robert, 2 Ben, 2 Scott, 3 Richard
• 3 A, 4 P, 3 R, 1 B, 1 S
• 2 Johansson, 2 Fleischman, 1 Armitstead, 4 Armstrong, 2 Armistead, 1 Atkinson

The surname can't be

Atkinson or Armitstead, since each of these appears only once, and Nick didn't know the answer until after the other two had spoken.

Similarly, the middle name can't be

B or S, since each of these appears only once.

## Deduction

1. Raj responds: No I do not. But I know they do not either.

The first name can't be Scott, Ken, or Robert, since each of these is associated with a unique middle or last name (B, Armitstead, and S/Atkinson respectively). So

it must be Ben or Richard. The only possibilities remaining now are Ben P Armstrong, Richard R Armistead, Richard A Armstrong, Ben A Armistead, and Richard P Armstrong.

2. Lisa responds : Hmm. I did not know before Raj spoke and I do not know now.

Naturally, Lisa knows everything in the previous item, being able to deduce it from Raj's statement just as we do. So the middle name can't be R, since there's only one R among the five names we've narrowed it down to.

3. Nick says: I did not know before, but now I know your full name.

Among the four remaining possibilities, there's only one unique surname. So the name is

If the "Armitstead" is a typo for Armistead, then the deduction runs as follows.

1. Now Ken is still a possibility, so there are 8 possible names instead of 5: Ben P Armstrong, Richard R Armistead, Richard A Armstrong, Ben A Armistead, Richard P Armstrong, Ken A Johansson, Ken P Fleischman, and Ken R Armistead.

2. In the 8 names above, none of the middle initials are unique, so we can't get any more info from Lisa's lack of knowledge.

3. There are two unique surnames in the above list of 8, and since Nick now knows the full name, it must be one of these: Ken A Johansson or Ken P Fleischman.

4. But now Raj still has no way of knowing the full name. Contradiction.

Thus "Armitstead" really wasn't a typo.

• I knew you would jump on this one Rand al'Thor. It is Logic afterall.
– DrD
Jan 2 '18 at 14:19

IF I were to teach someone to answer this question, I would tell them that this can be solved in either of two ways: by using Pattern Recognition or by using Word Logic.

I like to find patterns so I am going to do the Pattern Recognition first, and then use Word Logic to check my answer.

PART I-Solve the problem: (Using Pattern Recognition)

Group the names by first name so that you have:

• Ken A
• Ken P
• Ken R

• Ben P

• Ben A

and so on.

When you do this, you find that the only two unique First names and Middle initials are: Scott B and Robert S

Looking at the last names of these chaps, you see that Scott's last name is Armstrong and Robert's last name is Atkinson. There are 4 Armstrongs and only 1 Atkinson.

So, pattern recognition indicates that the unique name is:

Robert S. Atkinson.

Part 2, Starting point: None of the 3 people can say with any certainty what the name is as they each have only one piece of information.

Part 2, Step 1: However, when person 1 (Raj) says that he doesn't know, that tells us that the first name that he has been given is not unique.

Part 2, Step 2: When person 2 (Lisa) says that she doesn't know and that Raj's info doesn't help her, we know that the Middle initial that she has been given is not unique.

Part 2, Step 3: When person 3 (Nick) says that he didn't know, but does now, he knows that he holds the key to this problem; that is, his name is the unique identifier.

In summary, you could have solved the problem using one of these, but teachers always say to go back and check your answers in case you made a mistake! (Hope that I didn't, but I am very tired!)

• You can tell this isn't a correct solution because person 1(Raj) says he knows that the others don't know. Therefore his first name doesn't match any unique solution.
– Jay
Jan 3 '18 at 2:09