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purpleunicorn_Andi said:1001,1002, 2001,2002
Crazynutt said:[size=-1]A quick math riddle for you:
Question: Can you find all the numbers that can't be called blue numbers
between 1000 and 2000 and prove your answers.
[/size]
deaduser said:I think I know. Its almost all of them. You can do 1000 and 2000 cause they are even numbers that are multiples of 5, and you can do all the odd numbers.
With the rest of the even numbers you have to see if they are multiples of an odd number. example 1000/5=200 so then you can say 198+199+200+201+202=1000
here are some others
1001=500+501
1002=333+334+335
1003=501+502
1005=502+503
1007=503+504
1008=335+336+337
1009=504+505
1010=200+201+202+203+204
1011=505+506
1013=506+507
1014=337+338+339
1015=507+508
1017=508+509
1019=509+510
1020=339+340+341
1021=510+511
1023=511+512
1025=512+513
1026=341+342+343
1027=513+514
1029=514+515
................
2000=398+399+400+401+402
God is Gracious said:Here's a bit of help, odd numbers and multipules of odd numbers are already blue numbers.
For any odd number X, if X-1=Y, then Y/2+(Y/2+1)=X
For any multipul of 3, X, then (X/3-1)+(X/3)+(X/3+1)=X
For any multipul of 5, X, then (X/3-2)+(X/3-1)+(X/3)+(X/3+1)+(X/3+2)=X
So, since multipules of odd numbers and odd numbers themselves are out, then all that are left are powers of two. (2, 4, 8, 16, 32,)
HOWEVER, 2 can be eached by these numbers: (-1)+0+1+2
4 can be reached by this: (-3)+(-2)+(-1)+0+1+2+3+4.
In short, X can be reached by (-(X-1))+....+0+....X
God is Gracious said:The answer is 1024. If you allowed negative numbers then the answer becomes trivial.
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