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userofmath
Member since Aug-20-04
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Aug-20-04, 08:06 PM (EST) |
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"Is this possible?"
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Replace "?" with either "+" or "-"
You can not shuffle numbers.
Every "?" must be replaced with a "+" or "-" no blanks allowed (to prevent combining numbers.0?1?2?3?4?5?6?7?8?9=0 Is this possible? |
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Cino Hilliard
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Aug-25-04, 06:23 AM (EST) |
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1. "RE: Is this possible?"
In response to message #0
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>Replace "?" with either "+" or "-"
>You can not shuffle numbers.
>Every "?" must be replaced with a "+" or "-" no blanks
>allowed (to prevent combining numbers.
>
>0?1?2?3?4?5?6?7?8?9=0
>
>Is this possible?
No, not with 1-9. It works with 1-4, 1-8, 1-12 ...
The sum of 1..9 = 45 an odd number. You need an even number as
the sum so that a + a = sum and then a-a = 0. For 45 the best
possible choice is 23 + 22 = 45 but 23-22=1. For 1 to 8 the sum is
36. So 18-18=0. No matter how you construct 18 by adding numbers <=8
then subtracting the other numbers will get 0.
8+7+3 so -1-2+3-4-5-6+7+8 = 0
7+6+5
6+5+4+3
etc
Have Fun
CLH |
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Fendetestas
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Nov-03-04, 08:52 PM (EST) |
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2. "RE: Is this possible?"
In response to message #1
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It is of course possible if you can replace some ? with blanks: -1+2+34-5-6-7-8-9 = 0
-1+23+4+56+7-89 = 0
-1-2+34+56-78-9 = 0
-12+3+4+5+6-7-8+9 = 0
-12+3+4+5-6+7+8-9 = 0
-12+3-4-5-6+7+8+9 = 0
-12+3-4-56+78-9 = 0
-12-3+4-5+6-7+8+9 = 0
-12-3+45-6-7-8-9 = 0
-12-3-4+5+6+7-8+9 = 0
-12-34+56+7-8-9 = 0
1+2-34-56+78+9 = 0
1-2-34+5+6+7+8+9 = 0
1-23-4-56-7+89 = 0
12+3+4-5-6-7+8-9 = 0
12+3-4+5-6+7-8-9 = 0
12+3-45+6+7+8+9 = 0
12+34-56-7+8+9 = 0
12-3+4+5+6-7-8-9 = 0
12-3+4+56-78+9 = 0
12-3-4-5+6-7-8+9 = 0
12-3-4-5-6+7+8-9 = 0 I've written a very simple Maple program that allows you to visualize every 1?2?3?4?5?6?7?8?9 combination, where the ? stand for a '+', a '-' or nothing that equals a given number N. |
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