# Products

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## Rules[edit]

Fill in some cells with numbers.

Each number from 1 to X must appear exactly once, where X is twice the number of rows in the grid. Numbers cannot share a cell. Each row must contain exactly two numbers. Each column must contain exactly two numbers. (There are no similar restrictions on the diagonals.)

When given, the numbers below and to the right of the grid indicate the multiplicative product of all numbers in that row, column, or long dotted line diagonal, respectively. (The product of one number is the number itself; the product of no numbers is 1.)

(Rules and example from PGP IB)

### Rule variations[edit]

- In some puzzles, it is also required for the two main diagonals also to have two numbers.

## History of the puzzle[edit]

Probably first appeared on WPC 1996 under the name "Number Grid". The author of the puzzles is unknown.

## Appearances in the past WPCs[edit]

- WPC 2018/Round 13 (Knapp Daneben) by Jiří Hrdina
- WPC 2018/Individual Playoffs (Knapp Daneben) by Jiří Hrdina
- WPC 2016/Round 16 by Matúš Demiger