"Doubles" and "Pairs"
If a box has only two possibilities remaining, I call it a "double".
A PAIR of doubles can make some eliminations obvious (example below)
The "advanced" technique of eliminations called "chaining" requires doubles. It is discussed at length at other places of this blog.
Here is a puzzle that has 15 "doubles".
The "rule" is, if the same "double" appears in the same row, column, and/or group, its values can be eliminated from any other box in that row/column/group.
This is NOT the same as finding a "pair of pairs".
I confess that my distinction between the words "doubles" and "pairs" is indefensible. My only suggestion to help grasp my difference is to remind yourself that "finding doubles is easy." It's simply finding two and only two possibilities in a box. You don't care WHAT the values are when circling them.
Afterwards, you look to see if you find the SAME doubles in a row, column, or group.
With pairs of PAIRS:
Here's an example:
If a box has only two possibilities remaining, I call it a "double".
A PAIR of doubles can make some eliminations obvious (example below)
The "advanced" technique of eliminations called "chaining" requires doubles. It is discussed at length at other places of this blog.
Here is a puzzle that has 15 "doubles".
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| In row 6, it should be obvious that ONE of the two red-bordered boxes MUST be an 8, and the other must be a 2. Therefore, you can eliminate "8s" from that same row (H6), and also from the same group (B5 and C5) |
The "rule" is, if the same "double" appears in the same row, column, and/or group, its values can be eliminated from any other box in that row/column/group.
This is NOT the same as finding a "pair of pairs".
I confess that my distinction between the words "doubles" and "pairs" is indefensible. My only suggestion to help grasp my difference is to remind yourself that "finding doubles is easy." It's simply finding two and only two possibilities in a box. You don't care WHAT the values are when circling them.
Afterwards, you look to see if you find the SAME doubles in a row, column, or group.
With pairs of PAIRS:
- You actually consider one value, looking for it to occur exactly twice in a row/column/ and/or group.
- (THOSE BOXES DON'T HAVE TO BE DOUBLES! OTHER NUMBERS CAN APPEAR WITH THEM. If fact, that's often the point!)
- Look to see if a DIFFERENT value occurs exactly twice (in same row/group/column) in the same two boxes.
- Cross out both those values you if they appear elsewhere in the same Row/Column/ and/or Group.
- Cross out OTHER VALUES that may appear WITHIN that original pair of boxes you found.
Here's an example:
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| Pairs of Pairs. At first glance it looks like "doubles" were marked off as in the previous example. But notice that EVERY marked pair has an identical marked pair in the same row/ column or group. And, as shown in the case of the red-bordered boxes, there can be MORE than 2 numbers appearing in the box. The 2 and 8 were marked in those boxes because they are the only 2 and 8 in the column. One MUST be a 2, the other must be an 8. You can eliminate the 5 and the 7 from C7. This leads pretty quickly to a solution. C8 becomes the only 7 in its group (and its column). More answers follow. |
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