Shikaku: list what fits
Write down every rectangle each number could take. A number with one option takes it, and a cell only one number reaches belongs to that number.
How it works
A option for a number is a rectangle with the right area that stays on the grid and holds no other number. A 6 can be 1 × 6, 2 × 3, 3 × 2 or 6 × 1, slid to every position that still covers the 6.
One fit: if a number has a single option, draw it. Every rectangle you draw takes cells away from the numbers around it, so look at them next.
Only reach: every cell belongs to some rectangle. If just one number has an option that covers a cell, that number’s rectangle must include it. This is elimination done on cells instead of numbers.
Counting options quickly
List the shapes first: the ways to write the number as rows times columns. Then, for each shape, count the positions that cover the number. Cross out any that leave the grid or hold another number.
Primes help. A 5 or a 7 can only be a straight line, so it has few options.
Worth memorizing
An option: right area, on the grid, one number inside.
One option left: draw it.
A cell only one number reaches is that number’s.
Practice
0 of 4 rightHow many options does the ringed 6 have?
How many options does the ringed 3 have?
Which number must cover the ringed cell?
Which number must cover the ringed cell?