Two weeks ago, we shared a pair of brain teasers sent in by a PuzzleNationer who discovered these particular deduction and math thinkers in a book of riddles and puzzles.

Today, we’re going to share not only the solutions, but how we got there! Please enjoy this brief solve and tutorial, courtesy of brain teasers from your fellow PuzzleNationers!

[Image courtesy of SharpBrains.com.]

Brain Teaser #1: There is a three-digit number. All three digits are different. The second digit is four times as big as the third digit, while the first digit is three less than the second digit. What is the number?

Solution: 582

This is a fairly simple one, but if you’re unfamiliar with brain teasers, or uncomfortable in general with number puzzles, it can be off-putting. No worries, though! We’ve got you covered.

We know the second digit is four times as big as the third. That leaves only two options for those digits: 4 and 1 or 8 and 2.

If the first digit is three less than the second digit, it can’t be 4 and 1, because that would be 4 minus 1, or 1 for the first digit, and the first and third digits can’t be the same.

That means it’s 8 and 2 for the second and third digits. So if the first digit is three less than the second, the first digit is 5, and the three-digit number is 582.

Brain Teaser #2: When asked about his birthday, a man said, “The day before yesterday, I was only 25, and next year I will turn 28.” This is true only one day in a year – what day was he born?

Solution: He was born on December 31st and spoke about it on January 1st.

The wording in this one is especially important, because at first glance, this sounds impossible.

“Next year, I will turn 28.”

But if you look at the key word in what the man says — “turn” — the puzzle starts to unravel.

If next year, he will turn 28, this means that, at some point this year, he will turn 27. Which means he is currently 26.

Let’s look at what we know:

• Day before yesterday: 25
• Currently: 26
• This year (at some point): 27
• Next year: 28

Since he’ll be both 26 and 27 this year, the day before yesterday had to be last year.

Which means that yesterday was his birthday.

But at some point this year, he turns 27. That means both yesterday and the day before yesterday had to be last year.

Which leaves us with this timetable:

• December 30 (day before yesterday, last year): 25
• December 31 (yesterday, last year, his birthday): 26
• January 1 (today, this year): 26
• December 31 (later this year): 27
• December 31 (next year): 28

He was born on December 31st and spoke about it on January 1st.

Did you unravel one or both of these brain teasers? Let us know in the comments section below! We’d love to hear from you.

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