Answer to question 30 about the wrongly wired tea and coffee drinks machine

Answer to question #30

A drinks machine offers three selections - Tea, Coffee or Random but the machine has been wired up wrongly so that each button does not give what it claims. If each drink costs 50p, how much minimum money do you have to put into the machine to work out which button gives which selection ?

I found this puzzle whilst looking through my logs on a site that linked to mine called Mad Puzzles over at Blogspot. I liked it so i sort of stole it, but the answer is all mine....

There is a little twist in this. at first i was thinking if we buy all 3 then we will know at least one for certain, but i got caught in a loop when i started to think about how much it would cost to know the other two for certain. I went back to the question and spotted the trick. let's try again....
A drinks machine offers three selections - Tea, Coffee or Random but the machine has been wired up wrongly so that each button does NOT give what it claims. If each drink costs 50p, how much minimum money do you have to put into the machine to work out which button gives which selection ?

Here in lies the key. Each Button does NOT give what it is labled as. Meaning, for example, the button labled as Coffee can not be the Coffee button, so if it were to dispense coffee then it can only be the Random button. not the coffee button. in this case having established that the button labled Coffee is the random button we only have the buttons labled Tea and Random to work out, and only the designations Tea and Coffee left to assign. Since the button labled Tea can not be the Tea button it can only be the Coffee button. and the button labled Random must therefore be Tea....

Simple, however if the button labled Coffee had dispensed Tea we wouldn't have been so lucky, it could have been Tea or Random.

We need to start with the button labled Random.... Enough talking....

The Answer

For the first drink press the button labelled Random.

We know this is NOT the Random button so if it dispenses Tea it is the Tea button likewise if it dispenses Coffee it is the Coffee button. From here it is simple to work out the other buttons knowing that they can't be what they say they are.

Button labelled Random dispences Coffee:

=> Button labelled Random is Coffee button

Leaves buttons labelled Tea and Coffee to be either Tea or Random
Button labelled Tea can not be Tea so must be Random
=> Button labelled Coffee must be Tea

Button labelled Random dispences Tea:

=> Button labelled Random is Tea button

Leaves buttons labelled Tea and Coffee to be either Coffee or Random
Button labelled Coffee can not be Coffee so must be Random
=> Button labelled Tea must be Coffee

There are only two combinations each requires 50p

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