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All the Sons (How Many Brothers? in the UK version) is a puzzle in Professor Layton and the Last Specter.

Puzzle

One day while you're speaking to two boys of the same family, they tell you:

"I have a brother two years older than me."
"I have a brother three years older than me."

The next day, two boys from the same family tell you:

"I have a brother one year younger than me."
"I have a brother four years younger than me."

What is the minimum number of sons there could possibly be in that family?

Hints




Click a Tab to reveal the Hint.

Reading the information again while making a diagram might help you work out how many brothers there could be.


Then see if there is any way that number could be made smaller.

Most people mistakenly think that there must be four brothers.


Read the puzzle again. Does anything come to your attention that might be a clue to the actual number?

Why were they talking about their ages on the following day?


There might be something in that.

If the second conversation had happened on the same day as the first, the information would have been different. SO one of the brothers must have had a birthday! Which means...


Solution

Correct

Three brothers is correct!

The key to this puzzle is that the second conversation happened on the next day.

If it was the middle brother's birthday on the second day, the brothers' age differences would have changed as shown in the diagram above.

Actually, this can also work when it's either the youngest or oldest brother's birthday. Can you see how?

LS137S

A big thanks to http://professorlayton4walkthrough.blogspot.com