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Half as Old (Sisterly Sums in the UK version) is a puzzle in Professor Layton and the Unwound Future.

## Puzzle

US Version

Two sisters are talking about their ages:

"One year ago, I was exactly half as old as you," said the younger one.

The older sister replies: "Even one year from now, your age will be half my age. Here, look, if we split the numbers into two parts, top and bottom, they both give your age in a year's time."

"Hey, you're right. That's really cool!"

How old is the little sister?

UK Version

Two sisters are talking.
"One year ago, my age was exactly half your age", says the younger sister.
The older sister replies: "Even one year from now, your age will be half my age. Here, look, if we split the numbers into two parts, top and bottom, they both give your age in a year's time."
"Wow, you're right!"

How old is the younger sister now?

## Hints

Click a Tab to reveal the Hint.

US Version

Don't worry about their ages one year ago. The key is what their ages will be one year from now.

Think about what it means to divide a number into a top and bottom half.

UK Version

You don't need to worry about how old the sisters were a year ago. The important point is their age a year from now. What does "split the numbers into two parts" mean?

US Version

Have you figured out what it means to split the numbers into two parts, top and bottom?

From zero to nine, the only numbers that retain a numerical meaning even when they're cut in half are one and eight.

UK Version

Have you worked out what "split the numbers into two parts, top and bottom" means?

Think about the numbers 0-9. Of these, the only ones that retain a numerical meaning even when they're cut in half are 1 and 8.

US Version

If one year from now the older sister is one year old, the younger sister will also be one, so this can't be right.

If a year from now the older sister is eight years old, the younger sister will be zero, so this also can't be right.

It also doesn't work for 81 or 88...

UK Version

If the older sister were 1 year old next year, the younger sister would also be 1, so that can't be right.

If the older sister were 8 in a year's time, the younger sister would be 0, so that's wrong as well.

Thinking about it this way, it's also plain to see that it wouldn't work if the older sister were 81 or 88 either.

US Version

From Hint Three, you learned that one year from now the older sister will have to be either 11 or 18.

If she's 11, when you divide an 11 into a top and bottom half, you still get 11, so this doesn't work. The only option left is the older sister being 18 one year from now.

Now all you have to do is figure out the little sister's current age.

UK Version

From Hint 3, you know that the older sister will be either 11 or 18 in a year's time. Splitting 11 into two parts, top and bottom, gives you 11, which doesn't fulfil the conditions. The only remaining possibility is that the older sister will be 18 in a year's time.

All you've got to do now is work out the sisters' current ages.

## Solution

### Incorrect

US Version

Are you overanalyzing it? Try thinking about it from a different perspective.

UK Version

Don't think too hard - try changing your way of thinking instead.

### Correct

US Version

Correct!

The little sister is nine years old.

The older sister is 17. A year ago, the older sister was 16 and the younger was eight, so she was half the age of the older one.

A year from now, the older sister will be 18 and the younger one 10. If you divide an 18 into a top half and a bottom half, each one is a 10!

UK Version

That's right!

The younger sister is currently 9 and the older sister is 17.

One year ago, the older sister was 16 and the younger sister was 8, half her sister's age. One year from now, the older sister will be 18 and the younger sister will be 10. Splitting 18 horizontally gives you 10 twice.

A big thanks to http://professorlayton3walkthrough.blogspot.com