Did you solve it? Are you a puzzle thoroughbred?

Picture presenting the galloping white horse — 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