# April Fool Proof

The following is an illustrated proof for the April Fool's joke tough sudoku. The only technique employed on this page is Coloring. Coloring, as I use the term, means making an elimination by considering only 1 type of candidate.

You may wish to refer to previous blog pages to properly put this joke into perspective. Links to these pages are found to the right, under Previous Entries.

This page illustrates, in my opinion, the minimum number of deduced elimination steps that this puzzle requires to solve. Although many other steps are possible, they are not shown, as this puzzle is very easy!

The information on the following blog pages may be helpful:

The illustration of a forbidding chain used in this proof uses this key:

• black line = strong inference performed upon a set (strong link)
• red line = weak inference performed upon a set (weak link)
• candidates crossed out in red = candidates proven false
Strong and weak need not be mutually exclusive properties.

### Puzzle at start

A few Unique Possibilities are available here.

There is no need to make any of them to find the step that unlocks this puzzle.

### Possible 5s at puzzle start

The 5s form an interesting, but absurdly simple configuration from the beginning.

Find all the possible locations for 5 illustrated to the left.

There are many possible coloring eliminations available considering only candidate 5 from the start.

### Forbidding Chain (Alternating Inference Chain - AIC) on 5s (Coloring) at start

One possible forbidding chain on 5s that solves this puzzle is illustrated to the left:

• c3 == h3 -- h5 == b5 => b1,c6≠5
If either b1,c6 where to be 5, then h3=h5=5, which is not allowed!

The puzzle is now nothing but hidden and naked singles to the end.

### April Fool's Proof

1. Start at 23 filled - the given puzzle. Unique Possibilities to 27 filled. (UP 27).
2. fc on 5s: c6 == c3 -- b1 ==g1 forbids g6=5 UP 81
• Sets 2
• Max depth 2
• Rating .03 - Happy April Fool's Day!

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