December 2024 Puzzler

The addition problem in the figure here looks wrong, but it's actually correct. The secret is that each alphabet letter actually stands for a digit. The letter O does not necessarily represent the number zero, but we will insist that the leading digit in a multi-digit number should not be zero. (So neither T, F, nor E can be zero.) Your challenge is to figure out which letters represent which digits to make the addition correct.

There are actually four correct answers, and for credit, you need only find one of them. But if you want an extra challenge, try to find all four possibilities.

Solution to May Puzzler

I’ll get to a 35.0 miles per gallon average in 11 minutes and 28 seconds. There’s nothing tricky about the solution – it’s just a matter of interpreting and organizing the information.

Let’s say that I’ve used G gallons of gasoline in driving the 500 miles so far. Then

(500 miles) / (G gallons)  = 34.9 miles/gallon

So then G is really 500 / 34.9. This is about 14.33 gallons, but I’ll just keep calling it G to keep the formulas clean

Now I’m traveling 60 miles per hour at 40 miles per gallon currently, so every minute:

• I travel one more mile, and
• I use 1/40 gallon of gasoline.

Thus, after M minutes I will have traveled 500 + M miles total and used G + M/40 gallons of gasoline. So the equation that I want is

(500 + M miles) / (G + M/40 gallons)  =  35 miles / gallon.

This is easily rewritten and solved:

500 + M = 35(G + M/40) = 35G + (7/8)M
(1/8)M = 35G – 500

4000 (0.1/34.9) = 400/34.9 = about 11.4613

This is 11 minutes and (0.4613)(60) = 27.68 seconds, so 11:28 to the nearest second.

Correct Solvers

First correct solution: Alex Blumenfeld, NMR Lab Manager, U of I Chemistry

Second correct Solution: Marianne Milander, B.S. Microbiology and Animal & Veterinary Science 2023

Others:

• Mark Daily, B.S. Physics, 1981
• Greg Stenback, B.S. Geological Engineering 1984, M.S. Statistics 1987