Limca, Coke or Either?

Logic Level 2

Three buttons for drinks- "Coke", "Limca" or "Either" (Either Coke or Limca) are offered by a machine at the bus stop. But the machine has been wired up wrongly by the staff at the bus stop such that each button does not give what it claims. If each drink costs Rs. $10$ , how much minimum money do you have to put into the machine to work out which button gives which selection?

The answer is 10.

2 solutions

Vinayak Srivastava
May 12, 2020

Put Rs $10$ and push the button for "Either".

There are only 2 possibilities-it will give either Coke or Limca.

If it gives Coke, then the button named "Either" is for Coke, the button named "Limca" is for Either selection and the button named "Coke" is for Limca.
If it gives Limca, then the button named "Either" is for Limca. The button named "Coke" is for Either selection. And the button named "Limca" is for Coke.

Thus, you can make out which button is for what by putting just Rs $10$ and pressing "Either" selection first.

@Vinayak Srivastava Nice question 👍. Just a suggestion, but shouldn't the title be "Limca" instead of "Limka"?

Darsh Kedia - 1 year ago

What is Rs?

Joshua Olayanju - 1 year ago

@Joshua Olayanju Rs is the symbol of Indian Currency - The Rupee

Darsh Kedia - 1 year ago

Awesome question

Kumudesh Ghosh - 1 year ago

I am a huge follower of @Vinayak Srivastava and @Kumudesh Ghosh and @Vikram Karki and @Mahdi Raza. YOU GUYS ARE AWESOME 👏

Darsh Kedia - 11 months, 3 weeks ago

Lol thanks.

Kumudesh Ghosh - 11 months, 3 weeks ago

It is clear that once you know what the “Either” button does, you are done, but there are a few important points you should take note of:

So long as the “Either” button spits out a coke or a Limca, it Always does what it claims. That is the point of this button. The only two faulty buttons are therefore the “Coke” and the “Limca” buttons.
Based on the information given, the “Limca” button must always provide a coke, and the “Coke” button must always provide a Limca, since these buttons do not give what they advertise (“either” is not a third drink choice). In other words, neither of these buttons can serve as a stand-in for the “Either” button, since it can be anything.

Akeel Howell - 11 months, 2 weeks ago

Darsh Kedia
May 13, 2020

Put in Rs 10 and choose the option reading "Either".
There are only 2 possibilities => It will give either Coke or Limca (since we know that it is wrongly labelled).
If it gives Coke, then the "Either" button is for "Coke", the "Limca" button is for "Either" and the "Coke" button is for "Limca".
If it gives Limca, then the "Either" button is for "Limca". The "Coke" button is for "Either" and "Limca" button is for "Coke".

Hence, we can figure out the correct labels by spending just Rs.10 and choosing the "Either" button.

See,

"each button does not give what is claimed"

So, if you push "Either" you are guarenteed to get only one drink. Whichever you get, that button contains the other one, and the one left contains "Either".

However, if you choose any of Limca or Coke, you can't be sure what it contains, because you can have the option of "Either" also, so you need to use "Either" button only!

Vinayak Srivastava - 10 months, 3 weeks ago

Thank You for clarifying their doubt since they weren't ready to listen to me. (PS - I am a huge fan of yours)

Darsh Kedia - 10 months, 3 weeks ago

i was ready and also dont just assume what we r thinking

NSCS 747 - 10 months, 3 weeks ago

@Nscs 747 – i changed my mind after i wrote that solution

NSCS 747 - 10 months, 3 weeks ago

@Nscs 747 – Ok Sorry for assuming :)

Darsh Kedia - 10 months, 3 weeks ago

@Darsh Kedia – thats alright

NSCS 747 - 10 months, 3 weeks ago

Limca, Coke or Either?

The answer is 10.

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