What integers make 7,10,-1 and -4
Let the 4 values on the two double-sided cards be,
A, B
a, b
N.B. A and B cannot appear together, nor can a and b.
Combinations are.
A + a
A + b
B + a
B + b
Assign values (N.B. values of these sums can be assigned in different combinations)
A + a = 7 ------------- (1) A + a = 7 ------------- (1)
A + b = 10 ------------- (2) A + b = 10 ------------- (2)
B + a = -1 ------------- (3) B + a = -4 ------------- (3)
B + b = -4 ------------- (4) B + b = -1 ------------- (4)
(4) - (2), (3) - (1),
B - A = -14 B - A = -11
B - A = -8 B - A = -11
(The first combination of assignments didn't work, but the second combo did)
There are two combinations of assignments that work. These are,
A + a = 7 ------------- (1) A + a = 7 ------------- (1)
A + b = 10 ------------- (2) A + b = -4 ------------- (2)
B + a = -4 ------------- (3) B + a = 10 ------------- (3)
B + b = -1 ------------- (4) B + b = -1 ------------- (4)
We have here two sets of simultaneous equations, the solutions of which are,
A = 10 - b, B = -1 - b, a = -3 + b, b = b
A = -4 - b, B = -1 - b, a = 11 + b, b = b
i.e. b can take any value.
Ist card
1st side: 10 - b or -4 - b
2nd side: -1 - b
2nd card
1st side: -3 + b or 11 + b
2nd side: b