MATH Question?!?

Question

This is sooo hard.
I tried a million different ways!
please help me out!

here's the question :


Use the digits 0,1,2,3,4,5,6,7,8,9 to make the equations true.
Use each digit once.


2+_=_

_x_=_ _

_/_=2

_-1=_




thank you soo much:)!

Answer 1

Oooh! I like puzzles like these! Let me put pen to paper and tell you what I figure out.

2 + A = B
C x D = EF
G / H = 2
J - 1 = K

The only places where 0 will work are A, F and K. If we try putting it at A, then B becomes 2. There is only one place for 1 (at E). And the only digit that works with it is 8 (at F). Then C and D must be 3 an 6. But now there is no value that will work for G and H.

If we put 0 at K, then J is 1. Now the only places where 5 will work are at A, B or E. Trying A = 5 makes B = 7. But then we are limited where 6 can go. Or if we try B = 5, A = 3 Then we have a hard time filling C,D,E,F... and if we do then G and H are inconsistent.

This is the long way of saying that we should put 0 at F. That makes C or D be 5 and the other must be an even number. E will be half of that number. Let's put D = 5:

2 + A = B
C x 5 = E0
G / H = 2
J - 1 = K

7 can go at A or J now. If we put it at J, then K = 6. But then we will use up 1,2,4,8 at C,E,G and H. The remaining 3 and 9 won't work for A and B.

So we must put A = 7, making B = 9

2 + 7 = 9
C x 5 = E0
G / H = 2
J - 1 = K

Now we have three pairs that are doubles (1, 2); (3, 6); (4, 8). Pairs will go for C,E,G and H. The last pair must belong to J and K. Only 2 and 1 will work there because the difference is 1:

2 + 7 = 9
C x 5 = E0
G / H = 2
2 - 1 = 1

Finally we actually have two choices for where to put the pairs:

2 + 7 = 9
6 x 5 = 30
8 / 4 = 2
2 - 1 = 1

or:

2 + 7 = 9
8 x 5 = 40
6 / 3 = 2
2 - 1 = 1

And obviously we can switch C and D for a couple other possible solutions:

2 + 7 = 9
5 x 6 = 30
8 / 4 = 2
2 - 1 = 1

2 + 7 = 9
5 x 8 = 40
6 / 3 = 2
2 - 1 = 1

Take your pick!

Answer 2

I believe there are only two solutions:
2 + 7 = 9
5 x 6 = 30 (I guess you could switch 5 and 6 and say that's another)
8 / 4 = 2
2 - 1 = 1

The other:
2 + 7 = 9
5 x 8 = 40
6 / 3 = 2
2 - 1 = 1

Answer 3

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Answer 4

9

Answer 5

2+7=9
6*5=30
8/4=2
2-1=1

Answer 6

2+2=4
5x7=35
6/3=2
9-8=1

Answer 7

Wow....tricky!

Answer 8

wow that is confusing.................