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Shareware Overload Trio 2
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SOLUTION.DOC
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1993-10-28
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SOLUTIONS.DOC Page 1 of 3
THE ODD BALL SOLUTIONS
METHOD 1.
Theory - After the first 'weigh', think about groups of three
for the balls and change sides for the next 'weigh'.
Follow steps 1 thru 13 to get the idea.
1. Weigh 1 2 3 4 against 5 6 7 8
a. If scales are balanced - go to step 2
b. If right side is heavy - go to step 6
c. If left side is heavy - go to step 10
2. Weigh 1 2 3 4 against 5 9 10 11
a. If scales are balanced - go to step 5 (ODD BALL is 12)
b. If right side is heavy - go to step 4 (ODD BALL is heavy)
c. If left side is heavy - go to step 3 (ODD BALL is light)
3. Weigh 1 2 3 9 against 5 6 7 10
a. If scales are Balanced - ODD BALL is 11/light
b. If right side is heavy - ODD BALL is 9/light
c. If left side is heavy - ODD BALL is 10/light
4. Weigh 1 2 3 9 against 5 6 7 10
a. If scales are Balanced - ODD BALL is 11/heavy
b. If right side is heavy - ODD BALL is 10/heavy
c. If left side is heavy - ODD BALL is 9/heavy
5. Weigh 1 2 3 4 against 5 6 7 12
a. If scales are Balanced - OOOPS
b. If right side is heavy - ODD BALL is 12/heavy
c. If left side is heavy - ODD BALL is 12/light
6. Weigh 5 6 7 1 against 8 9 10 11
a. If scales are Balanced - go to step 8 (ODD BALL is 2 3 4 and light)
b. If right side is heavy - go to step 9 (ODD BALL is 1/light or 8/heavy)
c. If left side is heavy - go to step 7 (ODD BALL is 5 6 7 and heavy)
7. Weigh 1 2 3 5 against 6 8 9 10
a. If scales are Balanced - ODD BALL is 7/heavy
b. If right side is heavy - ODD BALL is 6/heavy
c. If left side is heavy - ODD BALL is 5/heavy
8. Weigh 2 5 6 7 against 3 9 10 11
a. If scales are Balanced - ODD BALL is 4/light
b. If right side is heavy - ODD BALL is 2/light
c. If left side is heavy - ODD BALL is 3/light
9. Weigh 1 2 3 4 against 9 10 11 12
a. If scales are Balanced - ODD BALL is 8/heavy
b. If right side is heavy - ODD BALL is 1/light
c. If left side is heavy - OOOPS
10. Weigh 1 9 10 11 against 2 3 4 8
a. If scales are Balanced - go to step 12 (ODD BALL is 5 6 7 and light)
b. If right side is heavy - go to step 13 (ODD BALL is 2 3 4 and heavy)
c. If left side is heavy - go to step 11 (ODD BALL is 1/heavy or 8/light)
SOLUTIONS.DOC Page 2 of 3
11. Weigh 1 2 3 4 against 9 10 11 12
a. If scales are Balanced - ODD BALL is 8/light
b. If right side is heavy - OOOPS
c. If left side is heavy - ODD BALL is 1/heavy
12. Weigh 1 2 3 5 against 6 8 9 10
a. If scales are Balanced - ODD BALL is 7/light
b. If right side is heavy - ODD BALL is 5/light
c. If left side is heavy - ODD BALL is 6/light
13. Weigh 1 2 5 6 against 3 7 8 9
a. If scales are Balanced - ODD BALL is 4/heavy
b. If right side is heavy - ODD BALL is 3/heavy
c. If left side is heavy - ODD BALL is 2/heavy
FLOW CHART SOLUTION
Top is left scales
1 2 3 4 - Heavy 1/heavy
------------- - Equal 8/light
| 9 10 11 12 - No Way
|
1 9 10 11 - Heavy 1 2 3 5 Heavy 6/light
--------------- - Equal - -------- - Equal 7/light
| 2 3 4 8 - Heavy 6 8 9 10 - Heavy 5/light
| |
| | 1 2 5 6 - Heavy 2/heavy
| -------------- - Equal 4/heavy
| 3 7 8 9 - Heavy 3/heavy
|
| 1 2 3 9 - Heavy 10/light
| -------------- - Equal 11/light
| | 5 6 7 10 - Heavy 9/light
| |
1 2 3 4 - Heavy 1 2 3 4 - Heavy 1 2 3 4 - Heavy 12/light
------- - Equal - --------- - Equal - --------- - No Way
5 6 7 8 - Heavy 5 9 10 11 - Heavy 9 10 11 12 - Heavy 12/heavy
| |
| | 1 2 3 9 - Heavy 9/heavy
| -------------- - Equal 11/Heavy
| 5 6 7 10 - Heavy 10/heavy
|
| 1 2 3 5 - Heavy 5/heavy
| -------------- - Equal 7/heavy
| | 6 8 9 10 - Heavy 6/heavy
| |
| 1 5 6 7 - Heavy 2 5 6 7 - Heavy 3/light
--------------- - Equal - --------- - Equal 4/light
8 9 10 11 - Heavy 3 9 10 11 - Heavy 2/light
|
| 1 2 3 4 - No Way
-------------- - Equal 8/heavy
9 10 11 12 - Heavy 1/light
SOLUTIONS.DOC Page 3 of 3
METHOD 2.
The Second Method is to make 3 weighs as follows:
WEIGHING LEFT SCALES RIGHT SCALES
First 1 2 3 4 5 6 7 8
Second 1 2 5 6 7 9 10 11
Third 1 7 9 12 4 5 8 10
Then if LEFT is heavy write a "1", If RIGHT is heavy write a "2" and
if the scales balance write a "0" and use the following table.
BALL HEAVY LIGHT
1 111 222
2 110 220
3 100 200
4 102 201
5 212 121
6 210 120
7 221 112
8 202 101
9 021 012
10 022 011
11 020 010
12 001 002