If you only use doubles, then guessing ONE answer may quickly lead to conclusions about OTHERS. The goal is to come up with a contradiction... like having two 5's in the same row, group, or column. That PROVES your guess was wrong.
The method cannot PROVE that your guess is RIGHT! That is.... you might have NO contradictions, but could still be wrong (unless you've filled in all the boxes).
(To get to the learning point, skip down to the puzzle with the doubles all circled)
PB Post 2014 04 26 Lvl 6 (Repeated lower down)
Kickoff: You can do all the 3s and all the 7's!
After filling in the pinks, simpler methods fail. Here's results:
PB Post 2014 04 26 Lvl 6 w27 Same as above, except the pink boxes are filled in.
(I was able to solve by coloring 8's. I ASSUMED that F1 = 8. This eventually led to a conflict, proving - in fact - that G1 = 8, and also three other 8's were determined. ) FINIS
GUESSING with doubles works for this puzzle.
PB Post 2014 04 26 Lvl 6 w27 Same as above, except the doubles are circled.
Guessing that C8=4 produces a conflict.
The conflict varies, depending upon the order of making conclusions. You might get that both D2 and G2 = 5. Or that D2 and D9=8, or other. No matter. Any conflict proves that C8 cannot equal 4, and so it must equal 5.
FINIS.
Below are three different paths that a user might have created, beginning with C8=4. All 3 paths result in a conflict. Many other conflicting paths could be created. (Interestingly, guessing that D2 = 5 or D2=8 produced no conflicts.)
PB Post 2013 01 19 Lvl 6 (Repeated lower down)
I used "Multi Colors" to eliminate 3 from C4. Possibly not necessary.
In row 1, there are 2 pairs of 2/7 which allows me to strike 9 from B1, and strike 3&5 from C1.
Then I was stuck
PB Post 2013 01 19 Lvl 6 w 39 Same as above, except the blue boxes are filled
Note: Using methods described above the 4 underlined numbers - in Grps 1 & 4 - can be eliminated as choices.
I could not find any chains, and I resorted to "Guessing".
PB Post 2013 01 19 Lvl 6 w 39 Same as above, except the doubles are circled, and initial "guess" is indicated.
Guessing that A4 = 3 leads to conflicts (after lots of analysis, including some of the 3-candidate boxes). This PROVES that A4 cannot equal 3, and A4 = 4. FINIS!
PB Post 2013 03 02 Lvl 6 (Repeated lower down)
PB Post 2013 03 02 Lvl 6 w 26 Same as above, except the green boxes are filled
Note: Using "simple" methods, the 5 underlined numbers (in rows 1 and 3) can be eliminated as choices.
To proceed, use a chain starting with the 8 in A3. Then C3, C8, D8, D3, D1, F1. This proves that F3 cannot contain 6. Therefore, F3 = 7 FINIS.
OR GUESSING that B2 = 6 leads to conflicts, which prove that B2 must equal 4. Hint: You only need to work columns A-D to get the conflict. Include some 3-choice boxes.
PB Post 2014 05 03 Lvl 6 (Repeated lower down)
Here is an account of the order that I followed in solving. Users may have a different experience.
1. There were 6 naked singles.
2. Two hidden 1's, then a hidden 5.
3. In Column A, I used single-line elimination to cross out some 5s.
4. In Column E, single-line eliminations got rid of some 9s.
5. In Column F, 4/7 doubles allowed me to make several eliminations and prove that F1 = 8
6. Found a hidden 8
7. In Column D, 3/4 doubles means D4 is not 4; D4 = 5
8. In Column E, single-line eliminations of 4s in groups 2 & 8.
FINALLY - with 39, simple techniques failed me. See next puzzle:
PB Post 2014 05 03 Lvl 6 w39 Same as above, except the green boxes are filled in.
Note: Using "simple" methods, the 10 underlined numbers can be eliminated as choices.
To Guess, you should circle all the doubles (after first eliminating as much as possible...the 10 underlined numbers)
PB Post 2014 05 03 Lvl 6 w39 Same as above, except doubles are circled.
Note: Using "simple" methods, the 10 underlined numbers can be removed as choices.
Guess that A2 = 4! Following the consequences, clashing results (shown lower down.) "Clash" is good! It PROVES that the original guess must be wrong!
The order that a user follows gives different results, but if you assume that A2 = 4, you will eventually run into a conflict.
Illustrated below is one of many possible clashes.
PB Post 2014 05 03 Lvl 6 w39 Same as above, except clash illustrated when assuming A2=4.
The path above results in two 4's in row 2. This PROVES that the assumption (A2=4) must be wrong! Therefore A2 must equal 3.
The remaining 38 boxes were filled using naked singles!
It was also possible to solve this puzzle by coloring 4's, beginning at B1. Four 4's get revealed after which naked singles finish up.
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