Space Cadet... here is a solution for your ball-breaker
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Label the balls 1 through 12.
Load the scales as shown:
SIDE1: 1,2,3,4
SIDE2: 5,6,7,8
if(SIDE1 heavier than SIDE2)
{
Load the scales as shown:
SIDE1: 1,2,5
SIDE2: 3,6,9
if(SIDE1 heavier than SIDE2)
{
Load the scales as shown:
SIDE1: 1
SIDE2: 2
if(SIDE1 heavier than SIDE2)
{
// Ball 1 is the odd-ball, and is heavy
}
else if(SIDE2 heavier than SIDE1)
{
// Ball 2 is the odd-ball, and is heavy
}
else if(balanced)
{
// Ball 6 is the odd-ball, and is light
}
}
else if(SIDE2 heavier than SIDE1)
{
Load the scales as shown:
SIDE1: 3
SIDE2: 9
if(SIDE1 heavier than SIDE2)
{
// Ball 3 is the odd-ball, and is heavy
}
else if(SIDE2 heavier than SIDE1)
{
// Impossible, should never happen
}
else if(balanced)
{
// Ball 5 is the odd ball, and is light
}
}
else if(balanced)
{
Load the scales as shown:
SIDE1: 7
SIDE2: 8
if(SIDE1 heavier than SIDE2)
{
// Ball 8 is the odd-ball, and is light
}
else if(SIDE2 heavier than SIDE1)
{
// Ball 7 is the odd-ball, and is light
}
else if(balanced)
{
// Ball 4 is the odd-ball, and is heavy
}
}
}
else if(SIDE2 heavier than SIDE1)
{
Load the scales as shown:
SIDE1: 1,2,5
SIDE2: 3,6,9
if(SIDE1 heavier than SIDE2)
{
Load the scales as shown:
SIDE1: 3
SIDE2: 9
if(SIDE1 heavier than SIDE2)
{
// Impossible, should never happen
}
else if(SIDE2 heavier than SIDE1)
{
// Ball 3 is the odd-ball, and is light
}
else if(balanced)
{
// Ball 5 is the odd ball, and is heavy
}
}
else if(SIDE2 heavier than SIDE1)
{
Load the scales as shown:
SIDE1: 1
SIDE2: 2
if(SIDE1 heavier than SIDE2)
{
// Ball 2 is the odd-ball, and is light
}
else if(SIDE2 heavier than SIDE1)
{
// Ball 1 is the odd-ball, and is light
}
else if(balanced)
{
// Ball 6 is the odd-ball, and is heavy
}
}
else if(balanced)
{
Load the scales as shown:
SIDE1: 7
SIDE2: 8
if(SIDE1 heavier than SIDE2)
{
// Ball 7 is the odd-ball, and is heavy
}
else if(SIDE2 heavier than SIDE1)
{
// Ball 8 is the odd-ball, and is heavy
}
else if(balanced)
{
// Ball 4 is the odd-ball, and is light
}
}
}
else if(balanced)
{
Load the scales as shown:
SIDE1: 9,10
SIDE2: 11,1
if(SIDE1 heavier than SIDE2)
{
Load the scales as shown:
SIDE1: 9
SIDE2: 10
if(SIDE1 heavier than SIDE2)
{
// Ball 9 is the odd-ball, and is heavy
}
else if(SIDE2 heavier than SIDE1)
{
// Ball 10 is the odd-ball, and is heavy
}
else if(balanced)
{
// Ball 11 is the odd-ball, and is light
}
}
else if(SIDE2 heavier than SIDE1)
{
Load the scales as shown:
SIDE1: 9
SIDE2: 10
if(SIDE1 heavier than SIDE2)
{
// Ball 10 is the odd-ball, and is light
}
else if(SIDE2 heavier than SIDE1)
{
// Ball 9 is the odd-ball, and is light
}
else if(balanced)
{
// Ball 11 is the odd-ball, and is heavy
}
}
else if(balanced)
{
Load the scales as shown:
SIDE1: 12
SIDE2: 1
if(SIDE1 heavier than SIDE2)
{
// Ball 12 is the odd-ball, and is heavy
}
else if(SIDE2 heavier than SIDE1)
{
// Ball 12 is the odd-ball, and is light
}
else if(balanced)
{
// Should never happen
}
}
} |
