# What numbers should replace the question marks? (square with digits)

What numbers should replace the question marks?

Every question mark can be replaced by digit from set {1,2,3,4,5,6,7,8}.

5 7 8 6 8 6
8 6 3 ? 7 4
2 ? 7 8 6 8
5 8 ? 4 5 ?
3 1 7 2 8 6
7 4 8 5 7 3

Source: The Complete Book of Intelligence Tests: 500 Exercises to Improve, Upgrade and Enhance Your Mind Strength by Philip Cartez

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I think the way to approach this is as follows:

First, notice that most of the digits appear the same number of times as their numerical values. For example, 1 appears 1 time, 2 appears 2 times and 8 appears 8 times. The only numbers that do not follow this trend are 4, 5, 6 and 7, which appear 3, 4, 5 and 6 times respectively. Therefore, these 4 numbers must occupy one of each of the questions marks.

The second thing to notice is that numbers of the same value cannot be adjacent to one another, not even diagonally. So, using this information, we can logically deduce where to place each number.

So, the next step is:

There is one place where 7 can go and that is R4C6. Similarly, 6 can only go in cell R4C3. Once those numbers are placed, the 5 can only go in R2C4, which leaves R3C2 for the 4.

The final grid:

| | | | | | |
|---|---|---|---|---|---|
| 5 | 7 | 8 | 6 | 8 | 6 |
| 8 | 6 | 3 | 5 | 7 | 4 |
| 2 | 4 | 7 | 8 | 6 | 8 |
| 5 | 8 | 6 | 4 | 5 | 7 |
| 3 | 1 | 7 | 2 | 8 | 6 |
| 7 | 4 | 8 | 5 | 7 | 3 |

• I had to use code formatting for the table, because apparently spoilers do not work with Markdown Table. If anyone knows a better way to present the information, feel free to edit! – Alaiko Jan 8 at 17:08