Math Is Fun Forum

Mellyyy

Guest

How to do this maths investigation

There are three different bugs: happy, sad and blank. Only one bug is needed to reporduced and each generation of bugs gives birth to two new bugs and died immediately.

- A happy bug produces a sad bug and a blank bug
- A sad bug produces two happy bugs
- A blank bug produces a happy and a sad bug
- Each eneration lasts exactly the same length of time
- In the beginning there was only one bug

Investigate the generations of bugs created showing how many of each type of bug at any stage.

So it says to use a table or spreadsheet instead of a tree diagram. How would you do this?

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: How to do this maths investigation

Make a table that looks something like this:

Generation  |  Happies  |  Sads  |  Blanks
-------------------------------------------------
       0         |      1        |    0     |     0
       1         |      0        |    1     |     1
       2         |      3        |    1     |     0
       3         |      2        |    3     |     3

And continue that for as long as you need to. I've started with a happy bug, but presumably you'd need to make 3 tables, one for each starting point.

Out of interest, how would you have done it with a tree diagram?

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Why did the vector cross the road?
It wanted to be normal.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: How to do this maths investigation

Here's a sad starting out table.
H0            S1            B0
H2            S0            B0
H0            S2            B2
H6            S2            B0
H4            S6            B6
H18           S10           B4
H24           S22           B18
H62           S42           B24
H108          S86           B62
H234          S170          B108
H448          S342          B234
H918          S682          B448
H1812         S1366         B918
H3650         S2730         B1812
H7272         S5462         B3650
H14574        S10922        B7272
H29116        S21846        B14574
H58266        S43690        B29116
H116496       S87382        B58266
H233030       S174762       B116496
H466020       S349526       B233030
H932082       S699050       B466020
Here's the BASIC program:

s = 1
h = 0
b = 0

'happy -> blank & sad
'sad -> 2 happy
'blank -> happy & sad
for gen = 1 to 22
print "H";h,"S"; s,"B"; b
hh = 2*s + b
bb = h
ss = h + b

s = ss
h = hh
b = bb
'repeat
next gen

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igloo myrtilles fourmis

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: How to do this maths investigation

Here's a blank-starting-out table:
H0            S0            B1
H1            S1            B0
H2            S1            B1
H3            S3            B2
H8            S5            B3
H13           S11           B8
H30           S21           B13
H55           S43           B30
H116          S85           B55
H225          S171          B116
H458          S341          B225
H907          S683          B458
H1824         S1365         B907
H3637         S2731         B1824
H7286         S5461         B3637
H14559        S10923        B7286
H29132        S21845        B14559
H58249        S43691        B29132
H116514       S87381        B58249
H233011       S174763       B116514
H466040       S349525       B233011
H932061       S699051       B466040

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igloo myrtilles fourmis

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: How to do this maths investigation

Here's a happy-starting-out table:
H1            S0            B0
H0            S1            B1
H3            S1            B0
H2            S3            B3
H9            S5            B2
H12           S11           B9
H31           S21           B12
H54           S43           B31
H117          S85           B54
H224          S171          B117
H459          S341          B224
H906          S683          B459
H1825         S1365         B906
H3636         S2731         B1825
H7287         S5461         B3636
H14558        S10923        B7287
H29133        S21845        B14558
H58248        S43691        B29133
H116515       S87381        B58248
H233010       S174763       B116515
H466041       S349525       B233010
H932060       S699051       B466041

Notice that the number 932 thousand is turning up on all
3 of these happies, and 699 thousand, so cool...

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igloo myrtilles fourmis