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Subject: "Math"     Previous Topic | Next Topic
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Conferences The CTK Exchange Middle school Topic #74
Reading Topic #74
Russ
guest
Nov-21-02, 09:21 AM (EST)
 
"Math"
 
   If you can figure this out please reply to russk@shaw.ca
I need to solve this. You can only use theese numbers
(13,11,9,7,5,3,1,) to figure this out. The answer must total (14), you can only derive to this conclusion by only using five numbers adding or subtracting. eg.(y+y+x-z-z =14)
Thank you for your help in advance.


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Whymme
guest
Dec-02-02, 04:54 PM (EST)
 
1. "RE: Math"
In response to message #0
 
   Try to solve this puzzle first:

You have the numbers 10, 20, 30, 40 and 50. Try, by only using addition and subtraction, to get to 13.

Once you have found out that this is impossible, go back to your problem.

And if this was about a bet, there's a good chance that you've lost some money.

Whymme


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Umpire
guest
Dec-03-02, 00:40 AM (EST)
 
2. "RE: Math"
In response to message #0
 
   Russ - did you notice that you have only odd numbers to work with? If you are trying to combine five odd numbers using only addition and subtraction, you are going to end up with an odd result. Hence, you cannot get 14 as an answer.

It may help to write your available numbers this way:

13 = 2 * 6 + 1
11 = 2 * 5 + 1
9 = 2 * 4 + 1
7 = 2 * 3 + 1
5 = 2 * 2 + 1
3 = 2 * 1 + 1
1 = 2 * 0 + 1

If you add any two of these numbers, you will have an even result:

(2 * x + 1) + (2 * y + 1) = (2 * x) + 1 + (2 * y) + 1
= (2 * x) + (2 * y) + 2
= 2 * (x + y) + 2
= 2 * (x + y + 1)
= even!
for example, 13 + 5 = 18 (even)

If you subtract any two of them, you end up even again:

(2 * x + 1) - (2 * y + 1) = (2 * x) + 1 - (2 * y) - 1
= (2 * x) - (2 * y) + 1 - 1
= 2 * (x - y) + 0
= 2 * (x - y)
= even again!
for example, 13 - 5 = 8 (even)

Extending this thought a little, you can see that adding or subtracting four odd numbers is going to give you an even result. So will six. In fact, using ANY even number of odd integers is going to give you an even result. In your problem, you state that you must use any FIVE of the given integers. When you use the first FOUR of them, no matter which ones and no matter whether you add or subtract, you'll have an even number at that point. And when you either add or subtract that fifth odd number, you are going to have an odd final result.

14 is an even number. Your puzzle has no solution.

Hope that helps.


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