population prediction basic

After I read all the comments I feel tempted to give this basic problem a try. So, if I understand the problem correctly, the number of aliens living on day n is the number of aliens of the previous day (nobody dies) plus the number of eggs that hatch on this day. The latter is equal to the number of eggs created on day n - 5, which is the 3 times the number of aliens that lived on day n - 5.

So I opened my favorite spread sheet program and put a 1 in cells 0 to 4. In cell 5 and following I placed the expression

cell[n-1] + 3*cell[n-5]

which then produces the following series:

day  aliens eggs
0	1	3
1	1	6
2	1	9
3	1	12
4	1	15
5	4	24
6	7	42
7	10	69
8	13	105
9	16	150
10	28	222
11	49	348
12	79	555
13	118	870
14	166	1.320
15	250	1.986
16	397	3.030
17	634	4.695
18	988	7.305
19	1.486	11.265
20	2.236	17.223
21	3.427	26.313
22	5.329	40.398
23	8.293	62.313
24	12.751	96.108
25	19.459	147.777
26	29.740	226.716
27	45.727	347.910
28	70.606	534.849
29	108.859	823.173
30	167.236	1.266.504

That wasn't that hard and didn't even take a C++ program to solve, once all aspects of the problem were correctly understood. And there are a few details that still need better specification, e.g. does the alien who lands first, produce three eggs on the very day of his landing, or the day after? Or, if m eggs hatch on a particular day, do we count the number aliens before or after these eggs hatch? So, with all due respect, as a student I would hope for a more precise statement of a problem than the one given.

Here's an SQL Server Recursive Common Table Expression to do it:

WITH cte AS
(
	SELECT -1 [Day] , 1 [Aliens] , 0 [+1] , 0 [+2] , 0 [+3] , 0 [+4] , 0 [+5] , 0 [Eggs]
UNION ALL
	SELECT [Day] + 1 , [Aliens] + [+1] , [+2] , [+3] , [+4] , [+5] , ( [Aliens] + [+1] ) * 3 ,  [+2] + [+3] + [+4] + [+5] + ( [Aliens] + [+1] ) * 3
	FROM cte
	WHERE [Day] < 30
)
SELECT * FROM cte

Sorry to use a second answer here, the discussion is now pretty big.

Dear lecturer, tell me if I am right or wrong.

Your alien lays 3 eggs on day 1.
-If the eggs hatch on same day. On which day will they hatch ? My answer is day 1.
-If the eggs hatch 1 day after. On which day will they hatch ? My answer is day 2.
-If the eggs hatch 2 day after. On which day will they hatch ? My answer is day 3.
-If the eggs hatch 3 day after. On which day will they hatch ? My answer is day 4.
-If the eggs hatch 4 day after. On which day will they hatch ? My answer is day 5.
-If the eggs hatch 5 day after. On which day will they hatch ? My answer is day 6.

I guess everyone agree on this list :)

You posted this as a part of the solution:

Quote:

day 1 1 alien 3 eggs
day 2 1 alien 6 eggs
day 3 1 alien 9 eggs
day 4 1 alien 12 eggs
day 5 4 aliens 21 eggs
day 6 7 aliens 39 eggs

From this sequence, one can see that eggs laid on day 1 are hatching on day 5, which is after 4 days, when the problem state after 5 days.

PS: defeat not accepted because we all know you are wrong and infinite arguing have no interest. :-)

[update]

Quote:

what don't you understand about every FIFTH day ,

there is nothing to understand there because it is not the question. :)
The question is:

Quote:

An alien lays X egg each day and the eggs hatch after Y days.
If X is 3 and Y is 5, how many aliens

and "after 5 days" is not the same as on "fifth day".

My guess is 21646 31324 adult aliens and 9678 13953 just born on day 30 31.
My mistake: 1 day too early.

I used a spreadsheet to compute the value.
My rule is 1 event per day.
on day 1, the alien makes 3 eggs.
on day 6, the 3 eggs hatch.
on day 7, the 3 new born start to make eggs.

With X=1 and Y=1, it should give the Fibonacci sequence.

[Update]
Your sequence is wrong:

Quote:

day 1 1 alien 3 eggs
...
day 5 4 aliens 21 eggs

Eggs done on day 1 can't hatch 5 days later on day 5, there is 1 day missing.

Quote:

Quote:

day 4 1 alien 12 eggs
day 5 4 aliens 21 eggs

Your sequence imply that new born aliens are instantly able to make 3 eggs the same size as the one they just came out from. Your sequence also imply contain enough to make 1 baby and 3 eggs than contain enough to make a baby and ...

I think I know why nobody find your solution :)