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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.

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.

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.

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...

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.


Solution

Incorrect

Too bad!

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

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 ister 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.

UF150S

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

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