The young couple (in their early twenties) seated next to us started some introductory small talk, which somehow drifted towards recreational mathematics.

I've explained the term, told them about Perplexus, puzzles, tricks etc.

After a while the young man asked for a sample trick, based on math.

The following dialog ensued:

I: - # Please take your calculator(or smartphone), enter an integer number representing your current age in years
and add to it a number immediately following it, then add another number telling your age 2 years from now.

If your age were 44, you would get 44+45+46, ok?

The result (i.e. the sum of your three numbers) multiply by # 67.

He: - Done.

I: - You see a 4-digit number, unknown to me, - please reveal me just one digit, the second from left and I will "calculate" your age.

He: - The second from left digit is 8.

I (in no time): - You are 23 years old.

He: How did you find it out?

I: - Up to you to "solve" it and then you will amaze your new friends…

S I L E N C E

She: - I promise to solve it if you show it one more time addressing my age, but I ask you not to use the number 67.

I: - Agree. Same instructions as above - (between two # signs), but multiplying by **34** and asking to disclose the **last** digit.

She: - The last digit is: __ (she told me).

I (in no time): You are 24.

Both guesses were correct.

By the end of our meal the young lady fully reconstructed the process.

How about you?

What was the last digit She got?

Is the trick infallible?