Photograph: carton_king/Getty Images/iStockphoto
Earlier today I set you the following two puzzles: Here they are again with solutions.
1. Neigh bother
A stud owner specialises in breeding purebred Lipizzaners, Thoroughbreds and Shire horses. The breeder is asked by a client for a foal which is one third Lipizzaner, one third Thoroughbred and one third Shire. How can she breed one?
Solution
I like this puzzle because initially it sounds impossible. However, once you start breeding different generations, the answer follows easily.
Let the three breeds be x, y and z.
Generation 1. Breed each type together. There will be three types of foal, each which is half and half: xy, yz and xz.
Generation II: Combine two of these, say xy and yz, which will give you a foal that is xyyz, i.e half y, quarter x and quarter z.
Generation III: Combine xyyz with xz from generation 1, which creates xxyyzz, i.e a horse that is a third each breed.
I asked a horse breeder whether this was the type of thing a breeder might do. He said: “Only if they were young (you’re talking of at least 5-6 years a generation), wealthy - and nuts….” Oh well, who says maths needs to have application!
* * * IMPORTANT UPDATE * * *
I made a mistake! Sorry everyone. As a few of you who have reached out to me via email and social media have pointed out, there is no solution!
The error is that when you breed xyyz with xz, you DO NOT get xxyyzz. You have to compare like with like, and xz in this case should be written xxzz.
When you breed xyyz with xxzz you get xxxyyzzz, which is 3/8, 2/8, 3/8. Not three thirds.
There is no solution since every generation must have 2n distinct genes. There can be no solution since 2n is never divisible by three.
I apologise for this and in future I need focus more on screening the puzzles that are submitted!
2. Grey matter
Show this to your students. Ask them to guess what is behind the grey square? Most will be shocked by the answer:) If you know--don't spoil it! pic.twitter.com/cXZFt8YkZX
— Sunil Singh (@Mathgarden) September 12, 2022
Solution: If you were looking for a number (as I was when I saw this puzzle) you fell into the trap. I’ll let Sunil explain in his own words. And you will understand why I included the puzzle after one about horses. I was only trying to help.
So, the original photo had a chess knight where the grey square was--chess moving in an "L" shape. I thought it would be a "sly" puzzle to cover it. Notice I asked "what is behind?" I never said it was a number:) Each number is the number of moves to arrive at that square. https://t.co/Woh30TqrQB
— Sunil Singh (@Mathgarden) September 12, 2022
I hope you enjoyed today’s puzzles. I’ll be back in two weeks.
Thanks to Gilad Benjamini for the first puzzle and Sunil Singh for the second. Sunil is an author, speaker and math storyteller from Toronto.
I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.
I give school talks about maths and puzzles (online and in person). If your school is interested please get in touch.
