Dear quizzers,

After a way too long break I finally found the time for a new mathematical quiz on the occasion of my birthday.

Exactly three years ago I celebrated my 25th birthday in the Australian summer. As you all know they have the cutest animals down under: wombats, possums, duckbill platypi and roos. I loved all of them. But most interesting I found a strange breed of chameleons I was able to observe at an outback farm. These chameleons are either black or silver or pink. But they don’t change their color in order to disguise themselves like ordinary chameleons they changed their color according to some strange mechanism.

Whenever two chameleons of different colors snuggle up together they switch to the third color. Like when a black and a siver chameloeon snuggle they both turn pink and so on. When two chameleons have the same color, nothing happens. As these cute little creatures need a lot of love, this mechanism provided a wonderfull natural phenomen. They changed their color back and forth and i was immediately mesmerized. But suddendly i realized that as soon as all chameleons on the farm have the same color they will not be able to change their color anymore. Stricken with fear i counted them. There were 13 black, 15 silver and 17 pink chameleons.

Then I started thinking, if it might be possible that these 45 chameleons all have the same color at some point because they snuggle up in an awkward order. What do you think: Is it possible that this happens – even if it is very unlikely – or is it generally impossible? Please don’t hesitate to ask if you have anymore questions. I am looking forward to your answers and your arguments.

Full of love and numbers, your

Dr. Nancy

Photos by Sabine Reitmaier

*Related*

Kristin ShawdyIs there a prize!?!

I have an answer but I won’t dare ruin it for every one.

ShaneI have an Idea too, but won’t be able to explain it elegantly..

Zesty MangoIs this Mengenlehre?

produzentinI thought it was Farbenlehre

Zesty MangoDear Doc Nancy,

first of all, you look better than ever! Happy Birthday!

The problem seems to be that I would try to get two groups with an equal number first? obviously i want to turn all of them pink. so i’ll try to get 14 black and 14 silver. if i combine a pink with a silver, i have two more black. 15 black, 14 silver and 16 pink. and then, if i try to get 15 each, i again turn two silver. so it seems it doesn’t work as i’m always getting two new i cannot get equal numbers, because i would need to change a single one? i’m not sure if the problem ends there, but i say no it’s not possible.

Kristin ShawdyWhat I first thought when you described this interesting species of chameleons is how much they have in common with lesbians. For example when they mate, instead of reproducing, over time they simply start dressing alike. After this wardrobe transformation is complete they resemble each other so much that the physical attraction is gone and the cuddling is OVER. Then they never want to mate again until one of the two dates someone else and gets a MAKEOVER! This is the famous “lesbian bed death” epidemic you’ve probably heard of….

To solve this problem I started thinking about it backwards…What would it take to end up in this horrible situation where all the lesbians look alike and nobody sleeps with anybody anymore? Maybe you’re already thinking to yourself “I know!! Move to Germany!”.

In the situation with the chameleons you are absolutely right Zesty M., there would need to be exactly the same number of any of the two colours of chameleons at the same time. Then when all the perfectly paired desperate black/silver couples inevitably go home together at the end of a wild party on the outback farm, the next morning everyone would be pink.

To give a proof Zesty, try thinking about the differences between the number of chameleons of each of the three colours and how the differences change when there is a love connection.

Or maybe you’re sick of the math and want to try some biology:

http://en.wikipedia.org/wiki/Desert_Grassland_Whiptail_Lizard

produzentinOMG Miss Shawdy, it sounds like Doc Nancy can retire now! or did you just make out with her and turned her lezzie? where is she anyways? she sitting on that iphone again?

Doc Nancyi’ve been busy all day, sorry for the late response.

dear kristin: now that you mentioned it i think it probably were lezzies not chameleons. i took off my glases as shown on the first picture and so i probably mistook the girls for these gnarly creatures. and i constantly jabbered about chameleons to this man on the “farm”. but if the girls weren’t chameleons, he wasn’t a farmer, right? this is starting to get embarrassing…

dear zesty: once more you came up with some pretty smart thoughts. just as kristin recommends you already started thinking about it backwards: you thought about the situation before the all pink wonderland and then about the step before. but i would not say that you have already proved it. you just thought about some combinations. kristin’s hint might help you to fix your thoughts. oh and let me tell you this much: if it is possible to turn them all into one color then it is in particular possible to turn them all into pink.

dear shane: don’t hesitate to try to formulate your answer. if you doubt that it’s elegant, just sent a cute picture of you. that will be elegant enough.

Doc Nancyoh and there is a price: you can win a DIDGERIDOO. but you have to pick it up in frankfurt.

pros cannot win the price, sorry kristin. but your truly smart comments and hints are always welcome. so keep in touch with the kwizz and don’t hesitate to give further comments, anyway.

kikishe may be smart as hell with those numbers but that bitch is crazy, loved dancing with you!

Shanemy brain feels all curled up in black, silver and pink like the blow-outs round your neck (so no picture at the moment…) – but is this the way to go: the differences between the numbers of whatever coloured chameleons is 2,2,4. Whenever a cuddling takes place, one of these numbers stays the same because the number of the two cuddlers colours decreases by 1 so there is no change in the difference. The other two must always increase by 3. And we have to end up with the three differences of 45, 45 and 0 if we want all to have the same colour (which of course we dont!). I don’t see a way to decrease one of these differences down to zero because it either stays the same or increases by 3… the changing colour cuddling therefore is safe forever. is this what Kristin meant with her hint?

Doc NancyKiki i loved dancing with you and your two cute gogos, too.

Shane: Yes i think Kristin meant that you Should try to prove that differences between the three groups can never be so that you can match them so that only one color is left over. I just have to recheck if you have really proved it. Wait a sec please…

Doc NancyOk shane if my kwizzerz were average brained people i would except your solution As everything you write makes sense. But you riddle girls are so smart that i want to urge you to close the left over final gap: Why is it impossible to reach the differences 45, 45, 0 from the starting differences 2, 2, 4 when always one difference increases OR DECREASES by 3 And the other two stay the same? As soon as you fixed this gap you won the quiz. So hurry up miss smarty pants!

Mary MesshausenOooh! Ooh! I got it! Obviously the pink one is the cutest. Did I understand the kwizz correctly? I hate it when I misunderstand someting.

You look really amazing Doc Nancy btw… xoxo Mary

ShaneDear Nancy, sorry i’m late… you say the difference between the three groups can also decrease by 3. That means, differences should contain their direction. I imagine the numbers in a triangle now, and count the differences, say clockwise. But then, my starting differences would be 2, 2, -4. And the ending differences in the case of all pink would be 0,45,-45, in the case of black -45, 0, 45. Isn’t it? So I have to prove that with a simple +3/-3 operation one cannot go from 2 to 0, from 2 to 45, from -4 to -45 and so on… I would have nine equations in total to prove that none of the intervals from starting to ending differences for all three one-colour-cases is a multiple of 3. Is there not a simpler way to prove it?

Doc NancyDear shane i am in awe because of your brain power! 9 equations?!?! That sounds like pure sex to me. But i think you don’t need them. Actually all you have to do is put your smart arguments together: you say that the starting configuration is 2 2 -4 And the final configuration has to be 45 0 -45 or … Then you say that the differences between the starting and the final configuration has to be a multiple of 3. According to this you said that in each step the differences in- or decrease by 3 or stay equal. All you need now is Lüftung this together. Just skip your hot equation system. I know you can! Xo your deeply impressed Nancy

Doc NancyDear Mary your intuition is correct as always: of course the answer for a math quiz has to be pink! Thx for the flattering compliment. Xxx

ShaneOh no. Please, please, don’t tell me you mean matrices!! This is pure torture! The answer is pink! By the way I don’t know how to type them in this window.

Doc Nancydear shane, relax. you dont need any matrices. actually you have already solved the quiz: since the differences between the initial configuration and the possible final configurations are not a multiple of three it is not possible to reach a final configuration from the starting configuration. because the no only change by three or not at all in every step. CONGRATULATIONS! let me know when you will come and pick up the didgeridoo. or should bitz deliver it to T.O.? XO

ShaneDear Nancy, thank you! I come and pick it up because you have to show me how to play it… Big hug!