Monthly Archives: October 2011

Where the missing R1 went

Several times now, I have been sent or shown a variant of the following riddle, and asked if I can explain it:

Peter borrows R50 from John and R50 from James
 He spends R97 and gets R3 change
 He pays James and John R1 each and keeps R1
 He now owes them R49 each
 49 + 49 = R98 + R 1 in his pocket = R99
 Where is the missing R1?

Here is the explanation I provided, in case anyone else may find in helpful:

The sum at the end (R49 + R49 + R1) is a red herring. How Peter spends the money he borrowed and what change he holds from that is a completely separate issue to how he pays it back and what he still owes on his loan.

Look at this way:
Peter borrows R50 from John, R50 from James.
He gives John R1, gives James R1.

He still owes John R49, James R49.
So in total he still owes R98 of the R100 he borrowed.

He used R97 of that hundred, and R3 in change.

After paying R2 of his debt, he still has R1. He has to get R97 from elsewhere (he spent it already). R97 + R1 in his pocket is the R98 he owes John and James.

 

It’s the phrasing of the question that is out of whack.

R49 owed to James + R49 owed to John + R1 in his pocket is meaningless maths – that’s adding what he owes + what he owes + what he has. There is no physical R49 anywhere – it’s introduced in the story as a figure but it doesn’t physically exist. It represents what he owes, not a sum of actual money, so it can’t be added to the R1 that does exist.

What he owes cannot be mixed in an equation with the details of where the money went, they’re different issues.

The correct maths is either:

R49 owed + R49 owed + R1 paid back + R1 paid back = R100 (dealing purely with his debt, ignoring what exactly he did with the original R100)

OR

R97 spent + R1 kept + R1 returned + R1 returned (dealing purely with what he did with the money, ignoring the irrelevant matter of where it came from).

The reason it comes across as a missing rand is in the way it is phrased, but you can’t add R49 owed + R49 owed + R1 physically in your possession, since they are apples and oranges.

 

I hope this is helpful to someone.

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