[Guest]

Six brothers Br.P, Br.Q, Br.R, Br.S, Br.T and Br.U always take the same seat when they have their meals in the circular dinner table. The following figure displays their seat numbers.

		1

	  6   2

	  5   3

		4

The following is known:

1. The seat of Br.S is separated from Br.P's seat by precisely one of the other brothers.

2. The absolute difference of Br.R's seat number from that of Br.Q's and the absolute difference of Br.R's seat number from that of Br.S's are respectively either, 2 and 5; or, 5 and 2.

3. Br.Q's seat number is precisely 1 larger than that of Br.T's seat number.

4. Br.P's seat number is either 1 larger than or 1 smaller than Br.U's seat number.

Determine the respective seat numbers of the six brothers.

[Guest]

ans

		1 R

	 S 6   2 T

	 U 5   3 Q

		4 P

[Pickett]

Determine the respective seat numbers of the six brothers.

R = 1

T = 2

Q = 3

P = 4

U = 5

S = 6

Ah...AI beat me to it...nice

Edited March 23, 2009 by Pickett

[Guest]

1 - R

2 - T

3 - S

4 - U

5 - P

6 - Q

[Pickett]

1 - R

2 - T

3 - S

4 - U

5 - P

6 - Q

Your solution seems to break with this requirement:

3. Br.Q's seat number is precisely 1 larger than that of Br.T's seat number.

You have Q = 6, and T = 2...so...

[Guest]

My answer is the same as those posted. I just wanted to also post the reasoning that makes it the only solution.

From statement 3, we know that Q cannot be 1.

From statement 2, either R & Q or R & S are separated by a value of 5, which means they are in positions 1 & 6. This means that R has to be in position 1 or 6.

Let's guess he must be in 1. Then, from statement 2, Q & S must be in positions 6 and 3.

Let's put Q in position 3. From statement 3, that means T is in position 2.

From statement 1, P is in position 4, and that leaves position 5 for U.

If you place R in position 6, that only leaves position 4 for Q (3 for T), and P and U cannot be next to each other.

If you place R in position 1 and Q in position 6 (T in 5), you get S in position 3 and again P and U cannot be next to each other.

[Guest]

Six brothers Br.P, Br.Q, Br.R, Br.S, Br.T and Br.U always take the same seat when they have their meals in the circular dinner table. The following figure displays their seat numbers.

		1

	  6   2

	  5   3

		4

The following is known:

1. The seat of Br.S is separated from Br.P's seat by precisely one of the other brothers.

2. The absolute difference of Br.R's seat number from that of Br.Q's and the absolute difference of Br.R's seat number from that of Br.S's are respectively either, 2 and 5; or, 5 and 2.

3. Br.Q's seat number is precisely 1 larger than that of Br.T's seat number.

4. Br.P's seat number is either 1 larger than or 1 smaller than Br.U's seat number.

Determine the respective seat numbers of the six brothers.

R=1

S=6

T=2

U=5

Q=3

P=4

Explanation:

There is one brother between S and P, that is U

|R-Q|=2 and |R-S|=5 ie |1-3|=2 and |1-6|=5

Q=T+1 or 3=2+1

P=U-1 ie 4=5-1

Edited March 24, 2009 by parik