The Pattern in the Seating Chart
A exam hall seats candidates in rows following a rule the invigilator must infer. Row 1 has 6 seats, row 2 has 9, row 3 has 13, row 4 has 18. The invigilator needs to know how many seats row 6 will hold to plan supervision. A colleague suggests the rule is 'add 3, then 4, then 5, and so on'. A second colleague suggests 'each row is the previous row plus the row number plus one'. A third points out that only four data points exist, so any rule fitted to them is a guess. The hall's far wall limits any row to 30 seats.
1. Apply both proposed rules to predict row 6 and compare.
Read the worked answer
Rule 1 (add 3, 4, 5, 6, 7): row 5 = 18 + 6 = 24; row 6 = 24 + 7 = 31. Rule 2 (add row number + 1): row 2 = 6 + 3 = 9 ✓; row 3 = 9 + 4 = 13 ✓; row 4 = 13 + 5 = 18 ✓; row 5 = 18 + 6 = 24; row 6 = 24 + 7 = 31. Both rules give 31, and both fit all four points. The reasoning tests recognising that two different verbal descriptions can generate identical sequences, so agreement between colleagues is not independent confirmation.
2. How does the 30-seat wall limit bear on the prediction, and what should the invigilator do?
Read the worked answer
Both rules predict 31 seats in row 6, which exceeds the 30-seat limit. Either the rule changes near the wall (rows may cap at 30) or the pattern is wrong. The invigilator should not plan for 31; they should verify the actual hall layout or treat row 6 as capped at 30. The third colleague's caution is relevant: with four points, extrapolation is uncertain, and a physical constraint is stronger evidence than a fitted pattern. The reasoning tests whether a solver lets a hard constraint override a neat numerical trend.