May 13, 2024
Puzzler time.
This is not automotive. Here we go.
Our producer and our bookkeeper are sitting down right around tax time. They were looking over the books.
Our producer is balancing the checkbook. And our bookkeeper is looking over all the financial statements. The bookkeeper asks the producer what numbers he came up with on his end. The producer gives him a number. And the bookkeeper says, "That's not right."
So basically, the checkbook doesn't match the bank statements.
So our producer says, "Oh no. I guess I will have to do this all over again then..."
And the bookkeeper says, "Well, wait a minute, how much were you off by?"
And the producer says, "Let me see. We were off by $27 bucks."
Then the bookkeeper says, "Oh okay. You don't have to go add it all over again. I know what you did. You transposed two numbers."
So, the producer goes back and checks this, and sure enough, he had transposed two numbers. Where there was supposed to be a 74, he had written 47.
So the puzzler question is, what did the bookkeeper know that the producer didn't know?
Good luck.
So, how did the bookkeeper know that the producer had transposed two numbers?
Here is the answer.
So the arithmetic involved in the answer is: if you ever transpose numbers, you will end up with a sum, the difference in sums with is a multiple of 9. So in other words, when two adjacent numbers are transposed the resulting mathematical error will always be divisible by 9.
So the producer had wriiten 47, and it was supposed to be 74. And the difference between those two is 27. And 9 times 3 is 27.
So, the bookkeeper was able to tell what had happened, by hearing that the amount that the producer was off was 27.
That one was a hard one!
