This week’s Micro Softy is about Pete and his pills. Pete has been told to take two Munchoril pills and one Progofrin pill every morning. He takes exactly enough medicine with him to an isolated, rocky desert island for four days of rest and relaxation. He has also brought with him a hard cover copy of Non-Computable You by Robert J. Marks for relaxed but informative reading.

The boat will come to bring Pete back in four days. Until then, he is isolated. There are no other people, cell phones or pharmacies on the island.

He wakes up the first morning. The fresh oxygen-rich ocean air makes him dizzy, and he spills all his pills on the hard wood table in the kitchen. Unfortunately, the pills all look identical.

And it’s worse. Pete’s doctor cautioned him that if his medication dosages were off, it could lead to bone liquefaction. But skipping the medication was no better — he’d risk developing exploding elbow syndrome and a condition called hot dog fingers.

But Pete was clever. He survived the four days by taking the prescribed dosages of his medication.

How did he do it?

I’ll give the answer next Monday.

Solution to Micro Softy 43:  The Bookkeeper’s Trick 

Last Monday’s Micro Softy was a head scratcher. The bookkeeper’s trick deals with two lists of nearly identical numbers that, added up, result in different sums. One of the lists has a number that is inadvertently transposed. All we know is that the difference between the two answers is divisible by 9.

To see why 9 matters, consider the number 2345.  Transposing the second and third digits gives 2435, The difference is between the two numbers is 90 which is divisible by 9. So we know which numbers were transposed.

Image Credit: Olaf Speier - Adobe Stock

Illustrating the bookkeeper’s trick uses same math. Instead of x=2345, suppose the number x= abcd where each letter can be any number from 0 through 9. The number can be written as

x=  1000 * a + 100 * b  + 10 * c + d

Transposing the second and third digit gives y = acbd and the number

y =  1000 * a + 100 * c   + 10  * b + d.

Subtracting gives

y-x = 100 * (b-c) + 10 * (c-b)  = 90 * (b-c).

So no matter the value of b and c, the difference between x and y is divisible by 90 and therefore divisible by 9.

This example can be extended to apply to any example of a number where two adjacent digits are switched.

The difference is always divisible by 9.

The Micro Softy is a weekly feature of Mind Matters News. Here are the links to all the puzzles and answers to date:

Monday Micro Softy 43: The bookkeeper’s trick How could division by 9 explain what happens when numbers in a sum are inadvertently transposed? Micro Softy 42 is easier to solve if we recall the rules for dividing by each of these numbers in turn.

Image Credit: PRASERT - Adobe Stock

Monday Micro Softy 42: Bacteria multiply by dividing. But our puzzlers must solve this math question without doing either. And no calculators allowed. A hint for solving Micro Softy 41: Dividing an unusually shaped piece of land among four sons rather than three is easier if you think in terms of fractals.

Monday Micro Softy 41: King David’s sons’ puzzling inheritance. Solomon must figure out how to divide an oddly shaped piece of land equally among his brothers and himself. In Micro Softy 40, the critical question is not whether the watchman’s prophecy comes true or not; it’s how he came to learn the information anyway.

Monday Micro Softy 40: The fate of a false prophet. He wasn’t actually fired for being a false prophet but for something that his prophecy unintentionally revealed. The solution to Micro Softy 39 lies in considering an alternative possible meaning of a word commonly used in sports. You will also find links to Micro Softies 35 through 39 and their answers here as well.

And here are links to all the earlier Micro Softies

Monday Micro Softy 29: A funeral lament in four lines. The funeral director was puzzled by Dan’s description of his relationship to the deceased but there was no question that his grief was sincere Here, you will also find links to Microsofties 22 through 29.

Monday Micro Softy 21: Finding More of the Deadly Fentanyl Pills. There, you will also find links to Microsofties 11 through 20 as well.

At Monday Micro Softy 11: What Happened to That Other Dollar?, you will find links to the first ten Micro Softies. Have fun!