## Kiss those Math Headaches GOODBYE!

### Answer to Problem of the Week – 10/18/2010

Problem of the Week – Answer

Here again is the problem:

Katja and Anthony are on a sightseeing trip in the western United States. Beginning where they land in Santa Fe, NM, they drive 80 miles east to see the historic wild west town of Las Vegas, NM. Then they travel 50 miles north to visit the Kiowa National Grasslands . Next they drive 140 miles west to visit Chaco Canyon National Historical Park. Finally they journey 130 miles south to visit El Malpais National Monument. When they reach El Malpais, how many miles are they from their starting point in Santa Fe?

And here is the answer, sent in by Eric Trujillo, a computer engineer based in Salem, OR.

“After taking trip, the pair are 100 miles away from their SF starting point. I calculated by drawing a diagram and then using the Pythagorean theorem. Sides triangle were 60 and 80 miles, so hypotenuse = 100 miles, using 3-4-5 right triangle relationship.”

Thank you for that reply, Eric.

### Problem of the Week — Answer

Answer to the 10/1/2010 Problem of the Week

The problem:  Certain digits appear the same when reflected across horizontal lines or vertical lines. This week’s problem:  which two-digit numerals appear the same when reflected across a horizontal line? Which two-digit numerals appear the same when reflected across a vertical line? To answer, provide the list for the horizontal line and the list for the vertical line.

Solution, sent in by Jo Ehrlein, of Oklahoma City, OK:

Assuming you write the #1 with no serifs, then here are the single digits that are the same when reflected across a horizontal line:1, 3, 8, 0.  That means that the 2 digit numbers that are the same when reflected across a horizontal line are:  10, 11, 13, 18, 30, 31, 33, 38, 80, 81, 83, 88

2 digit numbers are only the same when reflected across a vertical line if both digits are the same AND the individual digits are the same when reflected across a vertical line. The single digits that meet that criteria are1, 8, 000 isn’t a valid 2 digit number.That means the 2 digit numbers that are the same when reflected across a vertical axis are 11 and 88.

Well done, Jo!

So the winner’s circle this week has one member:

Jo Ehrlein, Oklahoma City, OK

And, in Jo’s honor, here is our ceremonial picture of Oklahoma City, home of Ralph Ellison,author of Invisible Man,  if I recall correctly.

Oklahoma City, OK

Congratulations to everyone who worked on this problem. I had some detailed answers that were partially correct.

FYI:  Starting this coming week, I’m going to post the Problem of the Week on Monday for teachers who want to use it early in the week. Answers will be posted mid-week.