When a line of words and numbers is fed into a machine, the machine rearranges it step by step following a particular rule. An illustration of an input and its rearrangement is given below.
Input: crane saucer 73 60 59 80 harbour salad towel 49
Step I: 60 crane saucer 73 59 80 harbour salad towel 49
Step II: 60 towel crane saucer 73 59 80 harbour salad 49
Step III: 60 towel 80 crane saucer 73 59 harbour salad 49
Step IV: 60 towel 80 saucer crane 73 59 harbour salad 49
Step V: 60 towel 80 saucer 73 crane 59 harbour salad 49
Step VI: 60 towel 80 saucer 73 salad crane 59 harbour 49
Step VII: 60 towel 80 saucer 73 salad 49 crane 59 harbour
Step VIII: 60 towel 80 saucer 73 salad 49 harbour crane 59
Step IX: 60 towel 80 saucer 73 salad 49 harbour 59 crane
Step IX is the last step of this input.
Input: flag mosquito 83 valley 91 pepper 96 98 90 window
Following the same rule, which element will be third to the right of ‘window’ in Step IV for this input?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → flag
Compare each step of the illustration with the one before it. The machine fills the line from the left end, a number and a word by turns, starting with a number. In Steps I, III, V, ... the number with the smallest digit sum (the sum of its two digits) among the numbers not yet arranged moves to the next place from the left end; in Steps II, IV, ... the word that comes last in dictionary order among the words not yet arranged moves to the next place from the left end. The others keep their order.
Step I (a number): 60 (digit sum 6 + 0 = 6, the smallest left) moves to the first place from the left
Step II (a word): ‘towel’ (last in dictionary order among the words left) moves to the second place from the left
Step III (a number): 80 (digit sum 8 + 0 = 8, the smallest left) moves to the third place from the left
Step IV (a word): ‘saucer’ (last in dictionary order among the words left) moves to the fourth place from the left
Step V (a number): 73 (digit sum 7 + 3 = 10, the smallest left) moves to the fifth place from the left
Step VI (a word): ‘salad’ (last in dictionary order among the words left) moves to the sixth place from the left
Step VII (a number): 49 (digit sum 4 + 9 = 13, the smallest left) moves to the seventh place from the left
Step VIII (a word): ‘harbour’ (last in dictionary order among the words left) moves to the eighth place from the left
Step IX (a number): 59 (digit sum 5 + 9 = 14, the smallest left) moves to the ninth place from the left
After Step IX every one of the words and numbers is in its final place, so the arrangement is complete.
Apply the same rule to the input flag mosquito 83 valley 91 pepper 96 98 90 window.
Step I (a number): 90 (digit sum 9 + 0 = 9, the smallest left) moves to the first place from the left, giving 90 flag mosquito 83 valley 91 pepper 96 98 window
Step II (a word): ‘window’ (last in dictionary order among the words left) moves to the second place from the left, giving 90 window flag mosquito 83 valley 91 pepper 96 98
Step III (a number): 91 (digit sum 9 + 1 = 10, the smallest left) moves to the third place from the left, giving 90 window 91 flag mosquito 83 valley pepper 96 98
Step IV (a word): ‘valley’ (last in dictionary order among the words left) moves to the fourth place from the left, giving 90 window 91 valley flag mosquito 83 pepper 96 98
In Step IV, 90 window 91 valley flag mosquito 83 pepper 96 98, counting three places to the right of ‘window’ gives flag.
Why the other options are incorrect
Option (2) 83 — Incorrect. In Step IV, 83 is five places to the right of ‘window’.
Option (3) valley — Incorrect. In Step IV, ‘valley’ is two places to the right of ‘window’.
Option (4) mosquito — Incorrect. In Step IV, ‘mosquito’ is four places to the right of ‘window’.