## Introduction

NumberBlocks is a puzzle game which we have to determine the place of numbers by using given hints under some rules. Here we explain the rule of NumberBlocks with size 4×4 in detail for those who plays it for the first time. Then we demonstrate the solving process of an example puzzle.

In explanations, we call a horizontal sequence of boxes **row** and a vertical sequence of boxes **column**. We describe a position of a box as (1,1) using a row and a column number. For example, we call the colored box in the following image box–(2,3).

## Rule

There are three rules for NumberBlocks. Please remember them all.

- Each row contains each digit of 1–4 exactly once.
- Each column contains each digit of 1–4 exactly once.
- Each region surrounded by thick lines contains each digit of 1–4 exactly once.

Now we explain each rule in detail by using the example puzzle following.

### Rule 1

Each row contains each digit of 1–4 exactly once. This means that we cannot place same numbers in a row. In the example, a number 2 is placed in box–(2,4). So we cannot place another number 2 in box–(2,1), box–(2,2) and box–(2,3).

### Rule 2

Each column contains each digit of 1–4 exactly once. This means that we cannot place same numbers in a column. In the example, a number 2 is placed in box–(2,4). So we cannot place another number 2 in box–(1,4), box–(3,4) and box–(4,4).

### Rule 3

Each region surrounded by thick lines contains each digit of 1–4 exactly once. This means that we cannot place same numbers in a region. In the example, we can see four regions. Box–(1,1), box–(1,2), box–(2,1) and box–(3,1) forms one regions. A number 3 is placed in box–(3,1). Then we cannot place another number 1 in box–(1,1), box–(1,2) and box–(2,1).

## Tutorial

Here, we demonstrate a solving process of the example puzzle. This is not the only process to solve. We hope you will find other processes.

### Process 1

A basic technique to solve NumberBlocks is to find boxes in which a specific number should be placed. For that, we focus on given hints. First, we focus on a number 1 of box–(3,1). Then we fill boxes in which we cannot place a number 1 with a color by following rules.

Then, in each region, we have several boxes in which we can place a number 1. So we cannot decide which is the right box to place a number 1.

Next, we focus on a number 2 of box–(2,4). Then we fill boxes in which we cannot place a number 2 with a color by following rules.

This time, we notice that there is a box (surrounded by yellow lines) that number 2 is the only choice to be placed in. Because, by rule 3, we have to place a number 2 exactly once in the middle region. But, by rule 1, we cannot place a number 2 in box–(2,2) and box–(2,3). So box–(3,2) is the only box that we can place a number 2 in.

Now we decided the place of a number.

### Process 2

Next, let’s focus on row 3.

By rule 1, we know that each row contains each digit of 1–4 exactly once. But number 1, 2 and 4 are already placed in row 3. So box–(3,4) is the only box that we can place a number 3 in.

### Process 3

Please recall that we placed a number 2 in box–(3,2) in process 1. Then we can guess that this decrease the count of boxes in which we can place a number 2.

So let’s fill boxes in which we cannot place a number 2 with a color by following rules again.

By rule 3, we have to place a number 2 exactly once in the top left region. Now we notice that box–(1,1) is the only box that we can place a number 2 in. Let’s place a number.

### Process 4

Next, let’s fill boxes in which we cannot place a number 2 with a color again.

By rule 3, we have to place a number 2 exactly once in the bottom region. Now we notice that box–(4,3) is the only box that we can place a number 2 in. Let’s place a number.

### Process 5

Next, we focus on number 4. Then we fill boxes in which we cannot place a number 4 with a color by following rules.

Then, by rule 3, we notice that box–(1,4) is the only box that we can place a number 4 in. Let’s place a number.

### Process 6

Next, we focus on the top right region and column 4. Then, by rule 3, we notice that box–(1,3) is the only box that we can place a number 1 in. Moreover, by rule 2, we notice that box–(4,4) is the only box that we can place a number 1 in.

Now let’s place numbers.

### Process 7

Next, we focus on row 1 and column 3. Then, by rule 1, we notice that box–(1,2) is the only box that we can place a number 3 in. Moreover, by rule 2, we notice that box–(2,3) is the only box that we can place a number 3 in.

Now let’s place numbers.

### Process 8

Next, we focus on the top left region. Then, by rule 3, we notice that box–(2,1) is the only box that we can place a number 4 in.

Now let’s place a number.

### Process 9

Next, we focus on row 2 and column 1. Then, by rule 1, we notice that box–(2,2) is the only box that we can place a number 1 in. Moreover, by rule 2, we notice that box–(4,1) is the only box that we can place a number 3 in.

Now let’s place numbers.

### Process 10

Next, we focus on row 4. Then, by rule 1 or by rule 3, we notice that box–(4,2) is the only box that we can place a number 4 in. Finally, we reached the answer.

## Get Started

Most recently uploaded NumberBlocks puzzles are available on NumberBlocks.

Previous NumberBlocks puzzles are available on NumberBlocks Archives.