Spoiler Inside: Solution to Puzzle | SelectShow |
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The maximum number of combinations is all seven. Two black-white-and-tan puppies and one of each other colour combination satisfies the conditions.
The minimum number of combinations is three. One can not be the answer, because then, eight are of one or more colours which contradicts the premise that there are five of each colour. Two can not be the answer, because there is just no way to split up eight in two ways to have five of each colour. 7 and 1; and 6 and 2 contradict the premise there are five of each colour. 5 and 3 leaves three of one colour alone. 4 and 4 has no way of combining to make five. A solution for three is three black-and-white, 2 black-white-and-tan, and 3 tan-only. The colours can be rearranged to give a total of six solutions using this approach. |

Lynne MugfordI’ve become addicted to your puzzles which are run in the local paper – Kamloops This Week. I’ve struggled with your answer to the Puppies puzzle, #116, and am getting nowhere. Maybe you can point out the error in my reasoning? I think the maximum number of seven colour combinations is 10, and the minimum is 1. The minimum puzzled me since you are describing a group of puppies with certain characteristics so the minimum must be one. I believe the following combinations, the ten columns, do not contradict any of the premises.

Black 0 1 0 0 2 0 1 1 2 1

White 0 0 1 0 0 2 1 1 1 2

Tan 1 0 0 2 0 0 1 2 1 1

Black/White 3 2 2 3 1 1 1 1 0 0

Black/Tan 2 2 3 1 1 3 1 0 0 1

White/Tan 2 3 2 1 3 1 1 0 1 0

Black/White/Tan 0 0 0 1 1 1 2 3 3 3

Thank you for your assistance,

Lynne

Lynne MugfordOops, lost my formatting by cutting and pasting. Try this:

1) 2 Black/White/Tan, 1 Bl, 1 Wh, 1 Tan, 1 Bl/Wh, 1 Bl/Tan, 1 Wh/Tan

2) 3 Black/White/Tan, 1 Bl, 1 Wh, 1 Bl/Wh and 2 Tan

3 Black/White/Tan, 1 Wh, 1 Tan, 1Wh/Tan and 2 Bl

3 Black/White/Tan, 1 Tan, 1 Bl, 1 Bl/Tan and 2 Wh

5) 1 Black/White/Tan, 2 Bl, 1 Bl/Wh, 1 Bl/Tan and 3 Wh/Tan

1 Black/White/Tan, 2 Wh, 1 Bl/Wh, 1 Wh/Tan, and 3 Bl/Tan

1 Black/White/Tan,2 Tan, 1Bl/Tan, 1 Wh/Tan, and 3 Bl/Wh

8) 1 Bl, 2 Bl/Wh, 2 Bl/Tan, 3 Wh/Tan

1 Wh, 2Bl/Wh, 2 Wh/Tan, 3 Bl/Tan

1 Tan, 2 Bl/Tan, 2 Wh/Tan, 3 Bl/Wh

Lynne

Gene WirchenkoPost authorThank you for the feedback. It is good to hear that someone is enjoying my puzzles. Wait, you did not state that. You stated that you were addicted. BWAHAHAHA! I was similar with the puzzles of the late Dr. Jim Totten of TRU. I took over from him on the puzzles.

Puzzle #116 is not how many arrangements of puppy colorations. It is of the maximum and minimum number of the seven combinations that can occur. Whether it is one puppy with a particular coloration combination or whether it is more is irrelevant to the puzzle.

The number of arrangements would be another puzzle.

My wording could have been off a bit. Could you please point to what led you to believe what I did not intend? I like clear communication.

I also made a minor error in my solution which I will have to adjust. There are three (not six) different arrangements of the minimum solution example that I gave.

As to puzzle #118, since it is before the deadline, no comment.

Lynne MugfordHi Gene,

You’re obviously better at reading my intentions than I am in reading yours. My use of addiction did indeed imply pleasure or enjoyment (I think I stated that specifically to the editor of KTW), and I’m thankful you’re keeping the puzzle tradition going.

Now to the puzzle at hand… I think I finally get it. You were asking the reader to consider the homogeneity of the group of puppies. How many color combinations required to make up the most varied group, and the least varied group. Now that I understand the question I certainly concur with your answers of 7 and 3. What led me to believe what you did not intend was my haste, over-confidence – I did get the kittens puzzle correct – and no doubt personal challenges. I’m much more comfortable in the realm of numbers than in the world of words. On the bright side, I do learn from my mistakes and at the first opportunity I’ll be revisiting my answer to puzzle #118. I think it just might require more than the minute or so thought I gave to it, and as it is my first “answer” submission to your blog I would like to get it correct.

Thanks for taking the time to set my mind at ease, and enjoy the rest of your summer.

Lynne