Question 45
HardOriginal questionSeven people, Om, Priyanka, Rehan, Shalini, Tushar, Ujjwala and Vikram, live in a seven-storey building, one on each floor. The ground floor is floor 1, and the numbers increase going up. 'Above' or 'below' means anywhere above or below; 'immediately above' or 'immediately below' means the very next floor. The following is known:
1. Om lives on an even-numbered floor, but not on floor 2.
2. Exactly two people live between Om and Shalini.
3. Rehan lives immediately above Ujjwala.
4. Tushar lives below Priyanka, and Priyanka lives below Vikram.
5. Ujjwala lives above Om.
6. Vikram lives below Om.
One clue in the list turns out to be unnecessary: the same arrangement follows without it. Which clue is it?
Show the answer and explanation
Correct answer: D
Explanation
Drop the clue 'Ujjwala lives above Om' and try Om on floor 6. Shalini must then be on floor 3 (clue 2), leaving floors 1, 2, 4, 5 and 7.
Ujjwala and Rehan need two consecutive floors from these: 1 and 2, or 4 and 5. Either way only two floors below Om are left for Tushar, Priyanka and Vikram, who need three. So Om is on floor 4 even without the clue.
With Om on floor 4, the rest follows exactly as before, so the Ujjwala clue can go.
The other clues are all needed. Without the even-floor clue, Om 5 with Shalini 2 also fits; without the Rehan clue, Rehan and Ujjwala could swap floors 5 and 6; without 'Vikram lives below Om', Shalini 1, Tushar 2, Priyanka 3, Vikram 7 fits.
Worth noting
Hard questions of this type are about checking, not guessing: remove the clue and see whether a second arrangement appears.
- Concept
- Spotting a redundant clue by trying to break the solution
- Typical timeTypical
- 150 s
- Your timeYours
- —
Ten questions from Puzzles, at your own pace.