No need to go through all those permutations. You’ve already subtracted $1 from the total, leaving 10¢; therefore whatever the smaller price is, the larger price is $1 larger, $1.05 being $1 larger than 5¢. Just a riddle to throw people’s thinking off, like “Who is buried in Grant’s Tomb?” or “What’s the opposite of ‘Not In’?” (some people will answer “Out” when caught off-guard; sharp-minded people will answer “Not out”). Math that really gives me headaches is (in calculus) trigonometric substitution and integration by parts; the reason I mentioned physical chemistry earlier in this thread is because AFAICS, far more advanced math is needed to learn it (differential equations and beyond), but many colleges require only calculus II and math beyond that is merely elective according to the degree program . . .
Yep - I grew up using the simple "tricks". Like adding the integers 1 through 100 in a hurry. (1+100=101 50 X 101=5050)