If you have seen our free printable Tenner Grid puzzle or have read our introduction to Tenner Grid puzzles and aren’t sure how to get started, you are in the right place! In this post, we’ll take a walk through how to solve Tenner Grid Logic Puzzles and share tips for getting started 🙂

If you want to join in as we walk through this tenner grid puzzle, you can download the puzzle we are using below:

Tenner Grid SolvealongA quick recap before we move on. A Tenner Grid puzzle is played on a grid of cells which are arranged in columns and rows.

The sum of each column is detailed at the bottom of the grid.

## Tenner Grid Puzzle Rules

Here are the rules:

Each row contains one of each number from 1 – the total of cells in the row, in the example below it will be from 1 – 9. **There can be no repeated numbers in a row.**

Each column must add up to the total given. This is also a useful feature to remember when placing numbers:

There CAN be repeated numbers in a column.

No number can be adjacent to itself either vertically, horizontally or diagonally.

As with all good puzzles, the rules are simple – which results in a delightfully tricky puzzle to solve!

## Tenner Grid Puzzle Walkthrough

We are going to walk through the completion of a puzzle which is on a 9×6 grid, meaning each row should contain the numbers 1 – 9.

**Note: When I refer to ‘given numbers’ I mean the numbers which are on the grid to start.**

## 1/ Look for an Obvious Opportunities

Take a look at the grid and see if there are any obvious place to start. As we can see below, 5 of the 6 cells in the column are completed, therefore we can work out the missing number by taking the total of given numbers away from the total of the column. This gives us 6.

## 2/ Look for The Missing Numbers

We know that a 1 and 7 are missing from the second row. How do we know which goes where? The ‘no number can be adjacent to itself’ rule comes into play here. We cannot place the 7 in the end cell as this would put it adjacent diagonally to another 7. Therefore the missing number have to be placed like this in order to adhere to the rules:

## 3/ Work Out Where Numbers CAN’T Go

Row 3: Using the ‘No two numbers the same can be adjacent’ rule, we know that the number 6 cannot go in any of the three cells marked. Therefore I have ‘pencilled in’ **the only two places **where the 6 can go in this row.

## 4/ Use Arithmetic!

By doing a little arithmetic and looking at the possible combinations in the blank cells, we can narrow down our options. We’ll put this into practice now and see how it helps us eliminate possible numbers and find the correct numbers to be placed.

First, let’s look at the top row and identify the missing numbers. 3 & 4 are missing from this row, however we don’t know which belongs to which cell. I have pencilled them in for now.

Now let’s pencil in the numbers which can be placed in the blank cells in the column marked. To do this we must remember these two rules:

- Each row must contain one of each number between 1 – 9
- No identical number can be adjacent to itself, sideway, up and down or
**diagonally**

Therefore, taking this into account, we can narrow down the options. Tip: Keep an eye out for numbers in the adjacent diagonal cells and make sure not to include them as a ‘possible’

We therefore have the following option:

- The top cell will either be 3 or 4
- The first blank cell with either be 1,5,7 or 9 (note how it can’t be 4 because of the 4 in the adjacent diagonal cell
- The second blank cell will either be 4,7 or 8 (note how it can’t be 1 as this is the number of the cell below)

#### Calculations

It’s now time to do a little calculation. We know that the total value of the column must be 24.

The numbers already placed equal 10.

We know that the top cell with either be 3 or 4, meaning that the total so far will either be 13 or 14.

Therefore, in order to bring the total to 24, we need to find a combination of numbers from the possibless which will make either 10 or 11.

- 1, 5, 7, 9
- 4, 7, 8

It is impossible to create 10 from these numbers, and there is only one way we can make 11 (using the 7 from the first row and 4 from the second).

We can therefore confirm the numbers to complete this column as follows:

## 5/ Repeat

We can confirm the 4 at the top of the next row and follow the same process to complete the column.

We know the possible numbers for the first blank cell are 1,5,9 and the second 7,8,9.

With the total of the numbers placed being 16 and the total of the column being 30, we are looking for a combination which will make 14.

Again, happily there is just one option:

### A Note About Using Calculations

In the two examples above, there were only one possible combination to give the number we needed bring the value of the column to the column total. However, this isn’t always the case, so be prepared to find this doesn’t always help eliminate options.

Also, while you may be fortunate and find there are only one possible option when you are working on a column with three or more blank cells, you may find this technique works best when there are two blank cells only.

## 6/ Continue Filling Cells

We can continue filling cells using a combination of logic and arithmetic

Again, there is only one possible combination:

## 7/ Keep an Eye Out for New Opportunities

As more cells are completed, so new opportunities are revealed. For example, the recent confirmation of cells means we know how the end column should be completed.

## 8/ Continue Completing Columns

## 9/ Keep Checking Other Cells

Again, as more cells have been completed, so do new opportunities get revealed. In this instance, the confirmation of 9 that we did in the step above means we can now place 9 in the fourth row. Because we have placed 9 in the third row, we know where the 9 in the next row CAN’T go – thereby identifying the only place it can go!

And more – we know where 7 can’t go, thereby confirming the position of 7 and 8 in the fifth row:

and using arithmetic and logic we can complete more cells:

## Finish the Grid

We’ve finally got to the last four cells! We need to do a little maths to work these out, but when done, the grid will look like this:

## Tips for Solving Tenner Grid Puzzles

Here are some tips for solving tenner grid puzzles.

- Keep in mind the two key ways to work out the placement of the numbers – by calculating the value of the column and ensuring there’s one of each number per row not adjacent to the same number. Therefore if one method doesn’t open up any possibilities, try the other.
- Start with the rows and columns with the most given numbers
- As more cells are completed, go back and revisit cells which had many options, as some of these may have been eliminated
- Keep track of possible numbers using our handy worksheet!