matcafe

半夜無聊，解一下︰

Let x be the number chosen.
After steps 2 - 4, you get 50(2x+5)=100x+250

Let y = 1755 or 1754, depending the conditions of step 5.

now we have 100x+250+y.

Call your year of birth z.

Then the three digit number would be 100x+[(250+y)-z]

Thus, as long as 250+y is the current year, 250+y-z would be your age (this is where the 1755 or 1754 comes from).

Moreover, since x is between 0 and 7, the first digit number of 100x is just x.

Everything would work nicely as long as [(250+y)-z]< 100 (or someone older than 100 years old), otherwise there would be carrying of digits when adding to 100x.

Thus this game doesnt always work, but at least we are young enough.