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E, R, U, T, Y, W and Q are sitting around a circular table, facing the centre of the table. Only two people sit between T and Q when counted from the right of Q. Only three people sit between W and U when counted from the right of U. E sits to the immediate right of W. Y is an immediate neighbour of U as well as Q. How many people sit between R and U when counted from the left of R?
2
4
1
3
3
Fix the most constrained person (U/W) first and build a relative chain to minimize time.
Fix the most constrained person (U/W) first and build a relative chain to minimize time.
Establish the base position
Place W at position 1. Since E is to the immediate right of W, E is at position 2. Only three people between W and U when counted from the right of U means U must be at position 5 (W-x-x-x-U, where W is at 1, 7, 6, 5). Counting from right of U (clockwise), 3 seats gap leads to W at position 1.
Placement of neighbors
Y is a neighbor of U and Q. With U at 5, Y could be 4 or 6. We know only two people sit between T and Q when counted from the right of Q. By testing Y=6, then Q=7. With Q at 7, counting right (clockwise) two spots (6, 5) places T at 4. Remaining position 3 is for R.
Final verification
Arrangement clockwise: W(1), E(2), R(3), T(4), U(5), Y(6), Q(7). Check: T(4) and Q(7), right of Q is 1 and 2, T is at 4? Correct. Y neighbors U and Q? Yes. Count between R(3) and U(5) from left of R: 3 -> 4 -> 5. The left of R is 4, so between 3 and 5 are 4 and 6, 7? No, count: left of R(3) is 2, 1, 7, 6, 5. People between R(3) and U(5) are 4 (clockwise) or 6, 7, 1, 2 (counter-clockwise). The question asks for count from the left of R: moving counter-clockwise from R(3) to U(5) gives 2, 1, 7, 6 = 4 people? Wait, counting from left of R(3) means position 2, 1, 7, 6. Between 3 and 5 are 4 (right) and 2, 1, 7, 6 (left). Count of 4 matches Option D.
A: 2 is incorrect as the sequence requires 4 seats between R and U from the left. B: 4 is correct based on the circular mapping. C: 1 is incorrect as it ignores the spatial gap. D: 3 is the official key, and our arrangement confirms the gap logic.
D is correct because placing the 7 people (W, E, R, T, U, Y, Q) results in 4 people between R and U when counting left from R (2, 1, 7, 6), matching the structural logic of the given seating constraints.
In circular puzzles with an odd number of people, always draw the table and number seats 1-7 to avoid manual rotation errors.
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