I have a book of mathematical puzzles -- The Moscow Puzzles, edited by Martin Gardner -- and I'm struggling to make sense of the following puzzle. It seems utterly simple, yet the solution given seems completely wrong. Here's the puzzle and solution verbatim.
42. Tell "At a Glance"
Here are two columns of numbers:
123456789 1 12345678 21 1234567 321 123456 4321 12345 54321 1234 654321 123 7654321 12 87654321 1 987654321
Look closely: the numbers on the right are the same as on the left, but reversed, and in reverse order.
Which column has the higher total? (First answer "at a glance," then check by adding.)
The columns don't look like they have the same sums, but look closely: comparing digits, nine 1s match one 9; comparing tens, eight 2s match two 8s, and so on. Check by adding -- the sums are equal.
This solution seem totally wrong. The sum of the left column is 137174205, which is less than the value of the last number alone in the right column. We can also tell this without adding simply by flipping the order of left column: 1 matches 1, but 12 is smaller than 21, and ditto all the way down the remaining numbers. Also, when the solution says "comparing tens, eight 2s match two 8s", the eight 2s are indeed in the tens column, but the two eights are not.
Can anyone interpret the puzzle in a way that makes any sense? It's a pretty well-know puzzle book, for such a glaring error to get through.