Is There A Trick To The Answers?
Math Expression: Fill In Each __ With One Of The Digits From 1 Through 9 To Make A True Statement. Each Digit May Be Used Only Once. __/__x__+__x__x__/__+__x__=100 2,5,10,56, __-__/__+__=50
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There are 8 unique solutions* to the first problem, but only 4 different triples of addends:
1/2*6+5*7*8/4+3*9 = 3+70+27 = 100
4/1*8+2*3*5/6+7*9 = 32+5+63 = 100
4/6*9+2*5*7/1+3*8 = 6+70+24 = 100
4/8*6+2*5*7/1+3*9 = 3+70+27 = 100
6/2*9+5*7*8/4+1*3 = 27+70+3 = 100
7/1*9+2*3*5/6+4*8 = 63+5+32 = 100
7/4*8+3*6*9/2+1*5 = 14+81+5 = 100
8/3*9+4*5*7/2+1*6 = 24+70+6 = 100
No sequence of 2, 5, 10, 56 filling in the blanks of __-__/__+__ will make 50.
_____
* each of these solutions gives rise to 23 others by permuting the multiplicands. For example, the first solution given could also end in 9*3, or it could have 5*8*7 in the middle term. There are a total of 192 solutions out of 362,880 ways the digits 1-9 can be arranged.
1/2*6+5*7*8/4+3*9 = 3+70+27 = 100
4/1*8+2*3*5/6+7*9 = 32+5+63 = 100
4/6*9+2*5*7/1+3*8 = 6+70+24 = 100
4/8*6+2*5*7/1+3*9 = 3+70+27 = 100
6/2*9+5*7*8/4+1*3 = 27+70+3 = 100
7/1*9+2*3*5/6+4*8 = 63+5+32 = 100
7/4*8+3*6*9/2+1*5 = 14+81+5 = 100
8/3*9+4*5*7/2+1*6 = 24+70+6 = 100
No sequence of 2, 5, 10, 56 filling in the blanks of __-__/__+__ will make 50.
_____
* each of these solutions gives rise to 23 others by permuting the multiplicands. For example, the first solution given could also end in 9*3, or it could have 5*8*7 in the middle term. There are a total of 192 solutions out of 362,880 ways the digits 1-9 can be arranged.
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