¹Definition: A quick and easy way to find missing Big Numbers in Horizontal and Vertical Bands by seeing which lanes are already occupied.

²Look for: Numbers 1-9, one at a time, within a Band. Visualize how their houses eliminate cells in other Blocks of the Band.

³Consequence: Where only one empty cell is available for the number in a Block, enter that Big Number.
[More advanced: Also when two adjacent cells are available, enter hard-candidates.]

⁴Why it Works: Each Band must contain exactly three of a given number, each on its own lane. When a number is already in a lane in one Block it cannot go in that same lane in another Block of the Band.

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⁶To make life easier for us, in this technique we break the board up into horizontal and vertical bands in order to consider them one at a time:

⁷First we look at the horizontal bands:

¹¹Then we look at the vertical bands:

¹⁵There are three lanes in each band, and each of them must contain exactly one of the numbers 1-9.

¹⁶So, if we find a number in a lane, we can eliminate it as a possibility in the rest of the lane as well as in the block.

¹⁷Here is an example from a very easy puzzle. We start by looking for 1's in Horizontal Band 1. We find the first one at B3.
Then we visualize that cell's house (within the confines of Horizontal Band 1.) The darkened area represents all of the cells that cannot be a 1 (except for cell B3, of course, which already contains a 1.)

¹⁸Still looking for 1's in Horizontal Band 1, we find one in Block 2 at E1. We now visualize E1's house, just as we did for B3.

¹⁹With the visualization of these two houses we now see that there are only two possible cells in block three where a 1 could go: G2 and I2 (the only empty white cells in block 3.)

²⁰But, if we now look down the vertical columns for G and I we find a 1 at I7.
Visualizing its house reveals that there is only one cell left for the 1 to go in block three: G2. So, we fill in a 1 at G2.

²¹Next we look for 2's in Horizontal Block Row 1. We find one in Block 1 at C1, and visualize its house.

²²We find another 2 in this band at Block 2 in cell F2. Visualizing its house leaves only one cell in Block 3 that can hold a 2, so we don't need to do any column cross-hatching this time; we can just fill in a 2 in cell I3.

²³Looking for 3's in Horizontal Band 1, we don't find any in Block 1 this time, but we do find 3's in Blocks 2 and 3. We visualize their houses, and find that we are left with two possibilities for a 3 in Block 1: A2 and C2. However, when we look down these columns we find a 3 at C8. Visualizing its house, we are left with A2 as the only possible cell for a 3 in Block 1. So, we fill in a 3 in A2.

²⁴Up till now we have been finding two of the numbers we've been searching for in our Band. But when we get to number 4, we only find one occurence in Band 1: at G3. All is not lost, however; looking down the columns in Vertical Band 2 we find 4's at E7 and F6. Visualizing their houses, we are left with one cell available for a 4 in Block 2: so we enter a 4 in D2.

²⁵Having entered the 4 in D2, we now have our familiar situation of two numbers in the Band. So, we visualize D2's house, and then examine Block 1.
We find that there are two cells open for a 4 in Block 1: A1 and B1. There are no other 4's in these columns, so we can't narrow it down any further.

²⁶When this happens, we cannot enter a Big Number. We can't expect a technique to always yield results. There is something we can do here, with hard candidates but we'll save that for the next tutorial.

²⁷We move on to looking for 5's. We find a 5 in Block 2 at E3 and Block 3 at I1. This leaves an opening for a 5 in Block 1 at C2.

²⁸Your Turn!
Now it's your turn to try one! Look for 6's in Horizontal Band 1. Visualize their houses, then see what cell is available for the 6 in Block 3.
Remember that you can click on the Tools tab to make use of the Highlight House on Hover feature to help visualize the houses.