# Bowman Bingo

Bowman Bingo is a very advanced solving technique that analyzes the implications for a move in order to find a contradiction. It is named after Doug Bowman, who suggested this coloring approach, but was fully developed by Robert Woodhead, the author of the Sudoku Susser program. Andrew Stuart has also implemented this approach in his solver. MadOverlord outlined an algorithm for the technique suitable for use by human solvers. Since it involves the use of bingo chips, he dubbed the technique "Bowman Bingo".

Although the technique can be executed by human solvers, it is very slow in execution and relies for a great deal on chance to find a contradiction. The term Bingo is very well chosen.

## How it works

The technique uses a marking system to record the implications. With the help of a computer program that allows coloring of candidates, these colors can be used as markers. For manual solving, the player could use a set of translucent chips numbered 1 through 9, which are placed in the cells.

The markers show the state of each candidate in the pencilmark grid. The following marks can be used:

• Available (unmarked)
• Forced (blue)
• Initial (yellow)
• Disabled (red)
• Enforced (green)

### Step 1 - Select a candidate to be tested

The player first chooses an initial candidate. There is no guaranteed way to make the right choice. Although, choosing a candidate in a bivalue cell or bilocal unit gives a 50% chance of finding a Bingo. Choosing a candidate that has a lot of remaining peers may also prove useful, because it has a greater chance to produce some results.

The chosen candidate is marked as Forced. We are now entering a Bowman cycle.

### Step 2 - Select a candidate marked: Forced

If you enter this step in the first cycle, there is only one such candidate. Otherwise, there may be none, one or more. When there are none, clear all markers and return to step 1, otherwise choose one of the Forced candidates.

### Step 3 - Change the marker of the selected candidate

If there is only one marker present in the grid, mark the selected candidate as Initial, else mark it as Enforced.

### Step 4 - Implications of the selected candidate

Mark all remaining candidates in the selected cell as Disabled and do the same for all candidates in the peers of the selected cell that have the same digit as the selected candidate. These are the candidates that would be eliminated when the selected candidate were placed in the cell.

### Step 5 - Find new forced candidates

When there is only a single available candidate left in a cell, mark it as Forced. The initial version of Bowman Bingo did not inspect the houses, but it is also possible to mark a candidate as Forced when it is the last available candidate for that digit in its row, column or box.

### Step 6 - Check for contradictions

A contradiction exists when there are 2 candidates for the same digit marked as Forced, Initial or Enforced in a single house. If such a contradiction is found, eliminate the initial candidate.