Monday Micro Softy 42: Bacteria Multiply by Dividing
But our puzzlers must solve this math question without doing either. And no calculators allowed.Here’s a big number:
x=810,180,810,333,180,810,180
Bacteria multiply by dividing. But you are not bacteria.
So here’s this week’s Micro Softy: Without dividing, multiplying or using a calculator — using only your knowledge of number theory — show that this number x is divisible by 2,3,4,5,6,9,10,12,15,18 20, and 30. Addition is allowed.
Solution to Micro Softy 41: King David’s Inheritance
Last week’s Micro Softy was about a track of land shown on the left in Figure 1. King David wanted to divide the land into four equally shaped tracts to give to four of his sons, including Solomon.
This is Solomon’s solution:
Interestingly, this pattern can be continued indefinitely as a fractal. If David’s four sons divide their tracks into four smaller tracts in the same way, the result is shown on the left in Figure 2. This division can be repeated as long as desired:
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 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
Image Credit: Aro - 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!
