## The 63 dollar question

By David Shaw, 26 June 2019

On Dr Vine’s desk there is some money.

- There are six pieces of Australian money.
- The money adds up to $63.

- There are no $1 coins.
- Each note is different from the others.

Can you work out what denominations are on the desk?

**Scroll down for the answer!**

## Brainteaser answer

First, the answer: a $50 note, a $5 note and four $2 coins will do it!

So how do we find the answer? First, you’re going to need a $50. Without it, there’s no way you can get close to $63 without having multiple notes with the same value.

Now, you need $13 from the remaining five pieces of money. There’s no way to do that with coins – five $2 coins is only $10. So you’ll need one more note, which could be either $5 or $10.

Let’s try a $10 first. With a $50 and a $10 on the desk, there are four more pieces of money, they add to $3, and none of them can be $1 coins. Four 50c coins only add to $2, and if you try using a $2 coin instead, you still won’t be able to find an answer.

If you try the $5 note, things work much better. Then the four remaining pieces of money add to $8, and that’s easy: four $2 coins!

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26 June, 2019 at 1:31 pm

I worked this out in an almost reverse order.

I noticed that $63 is an odd number and not allowing $1 means we need to get it to an even number somehow and the only way to do that is with a $5 note, leaving $58 behind.

I didn’t like the $50 part so I took care of that with a $50 note, leaving $8.

The easiest ways to divide that up is to either use [$1, $2, $5] (which isn’t allowed because of the $1) or [4 x $2]

Giving: $50, $5, $2, $2, $2, $2

26 June, 2019 at 2:25 pm

Nice!

You could also get an odd number of dollars with two 50 cent coins, right?

Still, it’s probably a fair assumption that the answer probably doesn’t use anything smaller than a dollar.

It’s quite fun trying to rewrite the puzzle for different currencies. It was much easier to phrase back in 1973, for instance – you can replace the ‘every note is different’ rule with ‘all six pieces of money are notes’!

28 June, 2019 at 3:23 pm

What about: $50 + $5 + $5 + $2 + .50 + .50 ?

28 June, 2019 at 3:37 pm

It adds up to $63, but it doesn’t work with the last rule:

Each note is different from the others.

Although thinking about it, you could always use a $5 coin…