Question #4351

you have to make 44 out of 6;7;8;and 9 each number has to exactly once and you are allowed only with the four basic operations (addition,substrction,multiplication,and division)you may use the same operators more than once

Expert's answer

6,7,8,9 … 44

Consider sum 6+7+8+9=30<44. Hence, we have to use product to get 44.

44=2x2x11 and 6=2x3, 7=7, 8=2x2x2, 9=3x3. Hence, we can’t get 44 only with products, because we don’t have 11.

Also, the only way we can divide is 8x9/6=(2x2x2x3x3)/(2x3)=2x2x3=12. And we can’t make 44 from 7 and 12, because 7+12=19<44 and 7 and 12=2x2x3 doesn’t consist 11.

Consider all possible products:

6x7=42 and 8,9

6x8=48 and 7,9

6x9=54 and 7,8

7x8=56 and 6,9

7x9=63 and 6,8

8x9=72 and 6,7

As we prove, we can’t use products.

With 42, 8 and 9 we can get 43=42-8+9.

With 48, 7 and 9 we can get 46=48+7-9.

With 54, 7 and 8 we can get 39=54-7-8.

With 56, 6 and 9 we can get 41=56-6-9.

With 63, 6 and 8 we can get 49=63-6-8.

With 72, 6 and 7 we can’t get anything similar to 44.

All other operations (I mean + or -) won’t give us better value.

Hence, we can’t get 44 from 6,7,8,9 by using allowed operations.

Consider sum 6+7+8+9=30<44. Hence, we have to use product to get 44.

44=2x2x11 and 6=2x3, 7=7, 8=2x2x2, 9=3x3. Hence, we can’t get 44 only with products, because we don’t have 11.

Also, the only way we can divide is 8x9/6=(2x2x2x3x3)/(2x3)=2x2x3=12. And we can’t make 44 from 7 and 12, because 7+12=19<44 and 7 and 12=2x2x3 doesn’t consist 11.

Consider all possible products:

6x7=42 and 8,9

6x8=48 and 7,9

6x9=54 and 7,8

7x8=56 and 6,9

7x9=63 and 6,8

8x9=72 and 6,7

As we prove, we can’t use products.

With 42, 8 and 9 we can get 43=42-8+9.

With 48, 7 and 9 we can get 46=48+7-9.

With 54, 7 and 8 we can get 39=54-7-8.

With 56, 6 and 9 we can get 41=56-6-9.

With 63, 6 and 8 we can get 49=63-6-8.

With 72, 6 and 7 we can’t get anything similar to 44.

All other operations (I mean + or -) won’t give us better value.

Hence, we can’t get 44 from 6,7,8,9 by using allowed operations.

## Comments

Assignment Expert24.09.14, 16:24Dear burak.

Thank you for correcting us.

burak18.09.14, 10:189/6 = 1.5

7-1.5 = 5.5

5.5*8=44

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