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Case

Brainteasers - Factory Control Room


Case prompt

FACTORY CONTROL ROOM

You are helping to run an understaffed factory. You need to know which button in the control room runs a large motor in a machining hall on the other side of the building. You cannot see or hear the motor from the control room.


Buttons can be pushed in to correspond to an “on” position. Pushed again, they pop out, corresponding to an “off” position.


You have already worked out that the button governing the motor must be one of three options. You are pressed for time and can only go across to check the machining hall once. After that, you cannot press any more buttons.


How can you figure out which button governs the motor? 



BURGLARY 

At Monday assembly, the headmaster of a school is alarmed to find that a valuable old trophy has been stolen from the assembly hall. The police think that the theft must have happened the previous afternoon and round up all the staff members with keys to the trophy cabinet as suspects, asking each to explain what they were doing at the time. The Groundsman claims he was pruning the roses. The Janitor says he was fixing a leaky radiator. The Head of Games reports he was out for a run. The Bursar was at the bank and the Nurse was attending to a sickly pupil.


The police immediately arrest the culprit and drag them to jail.


Which suspect was arrested and why?



ARCHIVES

You have been given the job of organising some in a natural history museum. The previous archivist was very incompetent and many boxes of documents have been labelled wrongly. You have three boxes of exhibits which you have been told definitely have the wrong labels.


One has snail shells, one oyster shells and one a mix of both. The labels for each have been mixed up amongst the three so that none match the contents.


To minimise disturbance to the exhibits you should open only one box and unwrap one shell.


Which box should you open to be able to allocate the correct labels to all three?


Comments

Brainteasers are brief questions designed to test candidates’ reasoning skills.


Each Question is designed to be solved in around 5-10 minutes.


If the candidate does not complete the brainteaser within 10 minutes, move on to the next.


Detailed solution

FACTORY CONTROL ROOM

You push two buttons into the “on” position and wait for a few minutes. You then push one of those two buttons into the “off” position and go across to the machining hall.


If the motor is on, it must be governed by the one button you left in the “on” position.


Feel the housing of the motor. If it is warm, then the machine has been running and it must be governed by the button you pushed “off” just before you headed over. If it is cold, then it has not been running at all and it must be governed by the final button that was never in the “on” position.



BURGLARY 

The Bursar was arrested. The police knew he was lying as the bank is closed on Sundays.



ARCHIVES

You take a shell from the box labelled as a mix of both. Since the “mixed” label definitely wrong, you know that if you unwrap a snail shell, the whole box must be snail shells and vice versa.


Say you did pick out a snail shell, and thus know the box labelled mixed is, in fact, full of snail shells. The box labelled oyster shells cannot have only oyster shells inside, as we know the label is wrong. Since the snail box is already accounted for, the box labelled oysters must actually be mixed. This means that the box labelled snail shells must, therefore, contain oyster shells.

Exhibits
This case doesn't have any exhibits.
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