BBC Radio 4  Puzzles for Today
BBC Radio 4  Puzzles for Today
So the Today programme on radio 4 have been broadcasting brainteasers for a while, which you can have a look at here:
http://www.bbc.co.uk/programmes/p057wxwl
It's an eclectic mix to say the least, but every now and again there's something interesting. #90 (November 3rd) has caught my attention today. The problem goes as follows:
Alien bees invade Earth. On the third and fourth days of its life, each bee gives birth to a live clone, then dies at the end of its fourth day. The invasion begins with one bee. How many bees are there at the end of the twentieth day?
Today’s #PuzzleForToday has been set by Dr Gihan Marasingha, Senior Lecturer in mathematics at the University of Exeter
(click this link for the published solution)
Ignoring the fact this puzzle is not welldefined  you need to make some assumption about the age of the initial invading bee  I cannot get the published solution under any permutation. I'll post my logic later, but I'd be interested to hear if anyone had any thoughts...
http://www.bbc.co.uk/programmes/p057wxwl
It's an eclectic mix to say the least, but every now and again there's something interesting. #90 (November 3rd) has caught my attention today. The problem goes as follows:
Alien bees invade Earth. On the third and fourth days of its life, each bee gives birth to a live clone, then dies at the end of its fourth day. The invasion begins with one bee. How many bees are there at the end of the twentieth day?
Today’s #PuzzleForToday has been set by Dr Gihan Marasingha, Senior Lecturer in mathematics at the University of Exeter
(click this link for the published solution)
Ignoring the fact this puzzle is not welldefined  you need to make some assumption about the age of the initial invading bee  I cannot get the published solution under any permutation. I'll post my logic later, but I'd be interested to hear if anyone had any thoughts...
Re: BBC Radio 4  Puzzles for Today
I'm with you Tom, I can't get a number anywhere near.
Re: BBC Radio 4  Puzzles for Today
In case anyone doesn't want this spoiled, select the following text with your mouse...
So there are 4 possible ages of bees: 0, 1, 2, or 3 days old  4 years old would mark the end of a bee's 4th year, which is when we're told it dies. At the end of day t lets denote the numbers of those bees by a(t), b(t), c(t) and d(t). The total number of bees is then just the sum of these 4 sequences.
The setup of the problem determines the following relations between the sequences:
d(t) = c(t1)
c(t) = b(t1)
b(t) = a(t1)
a(t) = c(t1) + d(t1)
The first three are simply ageing, the last is the cloning condition.
To obtain an answer, clearly you need to give an initial condition for a(0), b(0), c(0), d(0)  which is why this problem is not well defined. Presumably one of these is equal to 1, and the other three are equal to 0.
Anyhow, running these 4 iterations through, I get either: 48, 59, 70 or 38. None of these is remotely close to 200...
So there are 4 possible ages of bees: 0, 1, 2, or 3 days old  4 years old would mark the end of a bee's 4th year, which is when we're told it dies. At the end of day t lets denote the numbers of those bees by a(t), b(t), c(t) and d(t). The total number of bees is then just the sum of these 4 sequences.
The setup of the problem determines the following relations between the sequences:
d(t) = c(t1)
c(t) = b(t1)
b(t) = a(t1)
a(t) = c(t1) + d(t1)
The first three are simply ageing, the last is the cloning condition.
To obtain an answer, clearly you need to give an initial condition for a(0), b(0), c(0), d(0)  which is why this problem is not well defined. Presumably one of these is equal to 1, and the other three are equal to 0.
Anyhow, running these 4 iterations through, I get either: 48, 59, 70 or 38. None of these is remotely close to 200...
Re: BBC Radio 4  Puzzles for Today
My interpretation was that a(t)=c(t)+d(t) (not t1 on the RHS). However my maths still doesn't give me the quoted answer (I get 237).
Re: BBC Radio 4  Puzzles for Today
At the end of the day, the 3 days old bees die (if at the end of the first day of its life, it is 0 day old, then if it dies at the end of its fourth day, it's 3 days old), then d(t)=0 for any t.detuned wrote: ↑Thu 16 Nov, 2017 9:11 pmIn case anyone doesn't want this spoiled, select the following text with your mouse...
So there are 4 possible ages of bees: 0, 1, 2, or 3 days old  4 years old would mark the end of a bee's 4th year, which is when we're told it dies. At the end of day t lets denote the numbers of those bees by a(t), b(t), c(t) and d(t). The total number of bees is then just the sum of these 4 sequences.
The setup of the problem determines the following relations between the sequences:
d(t) = c(t1)
c(t) = b(t1)
b(t) = a(t1)
a(t) = c(t1) + d(t1)
The first three are simply ageing, the last is the cloning condition.
To obtain an answer, clearly you need to give an initial condition for a(0), b(0), c(0), d(0)  which is why this problem is not well defined. Presumably one of these is equal to 1, and the other three are equal to 0.
Anyhow, running these 4 iterations through, I get either: 48, 59, 70 or 38. None of these is remotely close to 200...
c(t) = b(t1)
b(t) = a(t1)
a(t)=b(t1)+c(t1) should fix your issues.
It works then for intial conditions a(1)=1, b(1)=0 c(1)=0 (the invasion begins with one bee, but it's not specified how old it is).
Fred

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Re: BBC Radio 4  Puzzles for Today
If anyone reads this far, spoilers really needn't be necessary.
OK, I can see where the 200 comes from.
If:
1) No bees die!
2) and his counting is out.
At the end of the 19th day, there are 179 bees <=4 days, and 21 > 4 days.
I suppose technically he says "how many bees" rather than "how many live bees"
But yeah, poor on many levels.
Answers to questions like this really should include workings. Just saying "It's related to the Fibonacci sequence" doesn't count as an explanation.
OK, I can see where the 200 comes from.
If:
1) No bees die!
2) and his counting is out.
At the end of the 19th day, there are 179 bees <=4 days, and 21 > 4 days.
I suppose technically he says "how many bees" rather than "how many live bees"
But yeah, poor on many levels.
Answers to questions like this really should include workings. Just saying "It's related to the Fibonacci sequence" doesn't count as an explanation.
Re: BBC Radio 4  Puzzles for Today
No, the dead bees are not counted.
Here is a table of alive bees population at the end of the 20 first days of invasion:
Fred
Here is a table of alive bees population at the end of the 20 first days of invasion:
Fred
Re: BBC Radio 4  Puzzles for Today
Re: BBC Radio 4  Puzzles for Today
Thanks for the explanation Fred, that makes sense

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 Posts: 2695
 Joined: Fri 18 Jun, 2010 10:45 pm
 Location: Edinburgh, Scotland
Re: BBC Radio 4  Puzzles for Today
I wasn't. My mistake was interperating the English. Thanks to the nonnative, not first language English speaker for putting me right . I was counting as days old, not days of life so had nowhere near the right number.PuzzleScot wrote: ↑Sat 18 Nov, 2017 12:01 amYeah, that makes more sense! At the end of the 4th day, the bee is already dead, but we were all counting it anyway.
Re: BBC Radio 4  Puzzles for Today
The solution briefly mentioned Fibonacci.
That was referring to the observation that the the number born today equals the number born 2 days ago plus the number born 3 days ago.
So that gives a Fibonaccistyle sequence, and from that sequence t18 + t19 + t20 = 200.
That was referring to the observation that the the number born today equals the number born 2 days ago plus the number born 3 days ago.
So that gives a Fibonaccistyle sequence, and from that sequence t18 + t19 + t20 = 200.