# Basic Strategy

# Advanced Strategy

Scanning can be done at the start and thru out the solution process. Scan the rows to identify where a line may contain a numeral by process of elimination. Perform the same scan on columns for the same numeral. If only one spot remains for the numeral in a given region then it must be that numeral.

Count up/down in an empty square using numbers found in the same row, column, and region. If there is only one missing number in the sequence, then that must be it. Usually you will find it can be one of two different numerals. If so, use the Subscript or Dot notation below.

In subscript notation, the potential numbers are "penciled' in. Doing so allows the use of the Matched Cells strategy below. Subscript notation can get messy and Dot notation maybe a better substitute when space is scarce.

Dot notation uses positional dots to indicate what numeral(s) can potentially be in a cell. Care must be taken to place the dot in the correct spot or it may be mistaken for an incorrect possibility. Negative dots can be used instead, marking what numeral(s) cannot be in a particular cell. Thus once eight numbers are eliminated, the only open spot must be the answer and can be marked over the underlying dots.

If two cells contain the exact two possible candidates, the other cells within the same row, column, or region of the two cells can eliminate those two candidates. The same applies to three cells containing three "matched" candidates. i.e. '12', '25', '125' appearing in a row allows elimination of 1, 2, and 5 from other cells in that row.

This approach is also known as the 'what-if' method. By solving with the assumption of a value, any conflicts invalidates that guess. Normally frowned upon because it digresses from logical solutions, it is nonetheless extremely valuable in higher level puzzles where the available information is extremely sparse. When a matched cell condition arises, using bifurcation on cells with 2 possible candidates allows for progress with minimal branching.

You can use "Snapshot" on this site to help you with bifurcation.

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