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What digits from 1-9 make a true satement you can only use each number once and you...

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fawn197710 | Student | eNotes Newbie

Posted August 30, 2009 at 5:38 AM via web

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What digits from 1-9 make a true satement you can only use each number once and you have to do it in this order:

 

__ /__ x__+__x__x__/__+__x__= 100

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kjcdb8er | Teacher | (Level 1) Associate Educator

Posted August 30, 2009 at 7:42 AM (Answer #1)

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Note that order of operations is suspended for this problem. A answer is:

((1/2*5+7)*6*4/9+8)*3 = 100

 

A computer algorithm was used to solve this problem. If you were just trying to guess, there are 362880 different permutations to try.

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neela | High School Teacher | (Level 3) Valedictorian

Posted August 30, 2009 at 2:18 PM (Answer #2)

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There is solution without bringing in extra mathematical operations  like brackets or paranthesis  but only with the given operations and given order of operations.The simplication of the solution is also strictly without disobaying the priority levels of operations in mathematics.

Only difficulty here  is it is a good exercise to go by trial and error method and try  and closing in towards a the solution.

The solution is : 8/1*4+2*3*5/6+7*9=100. It means by PEMDAS or PEDMAS  an expression like, ab/c  + def/g + hi  in algebra , where a,b,c,d,e,f,g,h,i can be any of the the values 1 to 9 without repetetion. As in algebra it can be treated as 3 terms with connector, +  summing to 100.

There are 3 terms on the left: 8/1*4 with a connector, + and followed by 2*3*5/6 with another connector, + and followed by 7*9.

Do the simplication operatios by PEMDAS (or PEDMAS)  priority :

First term: 8*1/4 = 32.

Second term :2*3*5/6= 5.

Third term:7*9=63

Therefore the sum (of the terms by PEDMAS) : 32+5+63=100.

So,8*1/4+2*3*5/6+7*9=100.

Hope this helps.

 

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