Addition Colour by Number Puzzle by Arithmetints - Free Printable

To solve this puzzle, we need to find the "missing piece" of the pattern. The grid is made up of squares, and each square contains math problems (addition). The last square in the bottom right corner is colored with tangram shapes instead of numbers. Our goal is to figure out which number belongs in that colored square by looking at the patterns in the other squares.

Step 1: Understand the Pattern

Let's look at how the other squares are organized. Each big square is divided into smaller triangles or sections. In most squares, there are addition problems like `40 + 33` or `12 + 61`.

If we calculate the sums for a few squares, we might see a relationship. However, a simpler pattern often exists in these types of puzzles: The sum of all the numbers in a specific position across the grid might be constant, or there is a row/column logic.

Let's try a different approach. Let's look at the sums inside each square.
Take the top-left square:
- $48 + 24 = 72$
- $40 + 33 = 73$
- $12 + 61 = 73$
- $36 + 36 = 72$

This seems complicated. Let's look for a simpler visual or numerical pattern.

Let's look at the center numbers or the total sum of each big square.
Actually, let's look at the structure of the grid itself. It is a $4 \times 4$ grid of large squares.
The bottom-right square (the 16th square) is the one with colors. We need to find what number or set of numbers should be there.

Wait, looking closely at the colored square, it is a Tangram. A standard tangram consists of 7 pieces that form a square. The colors are:
- Red (2 large triangles)
- Green (1 medium triangle, 2 small triangles? No, usually 1 medium, 2 small, 1 square, 1 parallelogram).
Let's identify the standard tangram pieces in the image:
- Two large red triangles.
- One medium green triangle? Actually, the green area looks like two small triangles and a medium one combined, or perhaps the standard layout.
- One yellow square.
- One orange parallelogram.
- One blue small triangle?
- One purple small triangle?

Let's re-examine the other squares. They don't just have random numbers. Let's calculate the sum of the two numbers in each small triangle/section for a single square to see if they equal a target number.

Square 1 (Top Left):
- $48+24=72$
- $40+33=73$
- $12+61=73$
- $36+36=72$
Average is around 72.5.

Square 2 (Top, 2nd from left):
- $35+38=73$
- $19+54=73$
It seems many sums are 73 or 72.

Let's check another square. Square 5 (2nd row, 1st column):
- $18+54=72$
- $22+50=72$
- $55+29=84$ -> Wait, $55+29=84$. This breaks the "all sums are 72/73" theory.
- $40+44=84$

Let's re-calculate Square 5 carefully:
- Top triangle: $18+54 = 72$
- Left triangle: $22+50 = 72$
- Right triangle: $50+23 = 73$
- Bottom triangle: $55+29 = 84$? No, looking at the image, the bottom section is split.
Actually, let's look at the diagonals or rows.

Let's try a different hypothesis: Each large square sums to a specific total.
Or perhaps the numbers correspond to the area or position of the tangram pieces?

Let's look at the colored square again. It's a standard Tangram puzzle. The question is likely asking: "What number is hidden here?" or "Calculate the value based on the tangram pieces."

However, there is a very common type of puzzle where the numbers in the triangles correspond to the number of letters in the color names, or something similar? No, the numbers are too big ($10$s and $20$s).

Let's look at the sums of the pairs in the colored square's neighbors to find a sequence.

Row 4 (Bottom Row):
Square 13 (3rd row, 1st col):
- $36+48=84$
- $50+32=82$
- $36+46=82$
- $14+68=82$
- $62+20=82$
Mostly 82s.

Square 14 (3rd row, 2nd col):
- $36+48$ is in sq 13.
In Sq 14:
- $19+65=84$
- $70+14=84$
- $39+44=83$
- $18+65=83$
- $50+44=94$? No, $50+44$ is in the next square.
Let's stick to the visible numbers in Square 14:
- Top: $19+65 = 84$
- Left: $70+14 = 84$
- Right: $18+65 = 83$
- Bottom: $39+44 = 83$
- Center/Diagonal: $50+44$ is actually in Square 15? No, the line separates them.
Square 14 has: $19+65$, $70+14$, $39+44$, $18+65$. And a central cross?
The lines divide the square into 4 triangles meeting at the center.
Sq 14 Sums:
- Top: $19+65 = 84$
- Left: $70+14 = 84$
- Right: $18+65 = 83$
- Bottom: $39+44 = 83$

Square 15 (3rd row, 3rd col - wait, the grid is 4x4. The colored square is at Row 4, Col 4? No.
Let's count the squares.
Row 1: 4 squares.
Row 2: 4 squares.
Row 3: 4 squares.
Row 4: 4 squares.
The colored square is in Row 3, Column 4? Or Row 4, Column 4?
Looking at the grid lines:
There are 3 horizontal lines dividing the main box into 4 rows.
There are 3 vertical lines dividing the main box into 4 columns.
The colored square is in the 3rd Row, 4th Column?
Let's trace:
Row 1: Top strip.
Row 2: Second strip.
Row 3: Third strip. The colored square is in the third strip from the top?
No, let's look at the bottom left.
Bottom-left square has: $14+68$, $62+20$, $35+47$, $26+56$, $65+17$, $19+75$, $50+44$.
This square is complex. It has many subdivisions.

Let's step back. This looks like a "Magic Square" variant or a pattern completion task.
Notice that in every white square, the addition problems result in sums that are very close to each other.
Let's calculate the sums for the square immediately to the left of the colored square (Row 3, Col 3? Or Row 4, Col 3?).

Let's assume the grid is 4x4.
The colored square is at position (4,4) (Bottom Right)?
Let's check the square at (4,3) (Bottom row, 3rd from left).
It contains:
- $50+44 = 94$
- $26+56 = 82$
- $65+17 = 82$
- $19+75 = 94$
- $35+47$ is in the square to its left?
Let's look at the square at (4,2) (Bottom row, 2nd from left).
It contains:
- $14+68 = 82$
- $62+20 = 82$
- $35+47 = 82$
- $26+56$ is in the next square.
Wait, the boundaries are tricky.

Let's try a different perspective. Look at the Tangram.
A standard tangram has 7 pieces.
The colored square has regions:
1. Large Red Triangle
2. Large Red Triangle
3. Medium Green Triangle? (Actually, in standard tangrams, the medium triangle is half the size of the large ones).
4. Small Yellow Square? No, the yellow piece is a square.
5. Orange Parallelogram.
6. Small Blue Triangle.
7. Small Purple Triangle.

Is there a number associated with each color?
Maybe the numbers in the surrounding squares hint at the values?

Let's look at the sums in the square above the colored one (Row 2, Col 4).
Square contents:
- $55+37 = 92$
- $70+22 = 92$
- $53+39 = 92$
- $19+73 = 92$
- $45+47 = 92$
- $16+57 = 73$? No, $16+57=73$.
- $20+53 = 73$
- $17+56 = 73$
This square has two sets of sums: 92 and 73.

Let's look at the square to the left of the colored one (Row 3, Col 3).
Contents:
- $27+46 = 73$
- $30+43 = 73$
- $49+43 = 92$
- $26+66 = 92$
This square ALSO has sums of 73 and 92.

Let's look at the square diagonally above-left (Row 2, Col 3).
Contents:
- $36+37 = 73$
- $29+44 = 73$
- $62+11 = 73$
- $19+54$ is in the previous square.
This square seems to be all 73s.

Let's look at the square at Row 3, Col 2.
Contents:
- $18+55 = 73$
- $50+23 = 73$
- $17+67 = 84$? $17+67=84$.
- $40+44 = 84$.
So this square has 73s and 84s.

Let's look at the square at Row 3, Col 1.
Contents:
- $18+54 = 72$
- $22+50 = 72$
- $55+29 = 84$
- $40+44 = 84$
So this square has 72s and 84s.

Let's look at the square at Row 4, Col 1 (Bottom Left).
Contents:
- $36+48 = 84$
- $50+32 = 82$
- $36+46 = 82$
- $14+68 = 82$
- $62+20 = 82$
This square is mostly 82s, with one 84.

Let's look at the square at Row 4, Col 2.
Contents:
- $19+65 = 84$
- $70+14 = 84$
- $39+44 = 83$
- $18+65 = 83$
- $50+44$ is in the next square?
Actually, the square at Row 4, Col 2 seems to have sums around 83/84.

Let's look at the square at Row 4, Col 3.
Contents:
- $50+44 = 94$
- $26+56 = 82$
- $65+17 = 82$
- $19+75 = 94$
- $35+47 = 82$ (from the left part?)
This square has 82s and 94s.

Now, let's look at the pattern of sums in the 4th Column (the rightmost column).
Row 1, Col 4:
- $16+57 = 73$
- $20+53 = 73$
- $17+56 = 73$
- $19+73 = 92$
- $45+47 = 92$
- $55+37 = 92$
Sums: 73 and 92.

Row 2, Col 4:
- Same as above? No, Row 2 Col 4 is the one I analyzed earlier as having 92s and 73s.
Wait, let's map the grid properly.
The grid is 4x4.
R1C4: Top Right.
Sums: $16+57=73$, $20+53=73$, $17+56=73$, $19+73=92$, $45+47=92$, $55+37=92$.
Pattern: Three 73s, Three 92s.

R2C4: Second Row, Rightmost.
Sums: $27+46=73$, $30+43=73$, $49+43=92$, $26+66=92$, $53+39=92$, $70+22=92$?
Wait, $70+22=92$.
So R2C4 has: Two 73s, Four 92s?
Let's re-read R2C4 from the image.
Top triangle: $27+46=73$.
Left triangle: $30+43=73$.
Right triangle: $53+39=92$.
Bottom triangle: $49+43=92$.
Center/Other splits: $26+66=92$.
And $70+22$ is in the square below? No, $70+22$ is in R2C4?
Looking at the image, $70+22$ is in the square at R2C4?
Actually, $70+22$ is in the square at R2C4's neighbor?
Let's look at the square below R1C4. That is R2C4.
It contains: $27+46$, $30+43$, $49+43$, $26+66$, $53+39$, and... $70+22$ is in the square to the left?
No, $70+22$ is in R2C4?
Let's look at the text orientation.
In R2C4, the text $70+22$ is vertical on the right edge.
Sum: $92$.
So R2C4 sums are: 73, 73, 92, 92, 92, 92.

R3C4: Third Row, Rightmost. This is the square ABOVE the colored one?
No, the colored square is in the bottom right corner.
Let's verify the position of the colored square.
It is in the 4th row and 4th column.
So the square above it is R3C4.
Let's analyze R3C4.
It contains:
- $55+37 = 92$
- $70+22 = 92$
- $53+39 = 92$
- Wait, I attributed these to R2C4 earlier. Let's look closer.
The square with $55+37$, $70+22$, $53+39$ is R2C4? Or R3C4?
Let's count rows from the top.
Row 1: Top strip. Contains $48+24$, $35+38$, $36+37$, $16+57$.
Row 2: Second strip. Contains $18+54$, $18+55$, $27+46$, $55+37$.
Row 3: Third strip. Contains $36+48$, $19+65$, [Colored Square?].
Wait. Look at the horizontal lines.
There is a thick black border around the whole thing.
Inside, there are thin black lines.
Let's count the horizontal dividers.
1. Below the first row of triangles.
2. Below the second row.
3. Below the third row.
This creates 4 rows.

Row 1 Squares:
1. TL: $48+24$ etc.
2. T2: $35+38$ etc.
3. T3: $36+37$ etc.
4. TR: $16+57$ etc.

Row 2 Squares:
1. L2: $18+54$ etc.
2. M2: $18+55$ etc.
3. R2: $27+46$ etc.
4. R2-Far: $55+37$ etc.

Row 3 Squares:
1. L3: $36+48$ etc.
2. M3: $19+65$ etc.
3. R3: This square is WHITE?
Let's look at the image again.
The colored square is in the bottom right.
Is it Row 3 or Row 4?
Let's look at the left column.
Sq 1 (Top): $48+24$.
Sq 2: $18+54$.
Sq 3: $36+48$.
Sq 4 (Bottom): $14+68$.
So there are 4 rows.

The colored square is in Row 3, Column 4? Or Row 4, Column 4?
Let's look at the square to the left of the colored one.
It contains $50+44$, $26+56$, $65+17$, $19+75$, $35+47$.
This square is in the bottom row (Row 4), because it shares the bottom border with the square containing $14+68$.
So the square with $50+44$ is R4C3.
Therefore, the colored square is R4C4 (Bottom Right).

So we need to find the pattern for R4C4.
Let's analyze the sums in the surrounding squares to predict R4C4.

Analyze Row 4:
R4C1 (Bottom Left):
Sums:
$14+68=82$
$62+20=82$
$35+47=82$
$26+56=82$ (Wait, $26+56$ is in R4C2? No, looking at the boundary.)
Let's trace the boundary between R4C1 and R4C2.
R4C1 has: $14+68$, $62+20$, $35+47$.
R4C2 has: $26+56$, $65+17$, $19+75$, $50+44$?
No, $50+44$ is in R4C3.
Let's re-examine R4C2.
It contains:
$26+56 = 82$
$65+17 = 82$
$19+75 = 94$
$35+47$ is in R4C1? Yes.
$50+44$ is in R4C3? Yes.
So R4C2 has sums: 82, 82, 94. And maybe another one?
The square R4C2 is divided into 4 triangles?
Top: $26+56=82$.
Left: $35+47=82$ (from C1? No, the line is diagonal).
Actually, the division lines are consistent. Each square is divided into 4 triangles by diagonals, sometimes further subdivided.

Let's look at the dominant sums in each square.
R1C1: 72, 73
R1C2: 73
R1C3: 73
R1C4: 73, 92

R2C1: 72, 84
R2C2: 73, 84
R2C3: 73
R2C4: 73, 92

R3C1: 82, 84
R3C2: 83, 84
R3C3: 73, 92
R3C4: ?

R4C1: 82
R4C2: 82, 94
R4C3: 82, 94
R4C4: Colored

There is a strong pattern of 72/73, 82/84, 92/94.
These are pairs separated by 1 or 2.
72/73
82/84 (diff 2)
92/94 (diff 2)

Let's look at the location of these sums.
70s: Top half of the grid (Rows 1 & 2).
80s: Bottom half, Left side (Rows 3 & 4, Cols 1 & 2).
90s: Right side?
R1C4 has 92s.
R2C4 has 92s.
R3C3 has 92s.
R4C2 has 94s.
R4C3 has 94s.

It seems the numbers increase as we go Down and Right?
Or maybe they follow a diagonal pattern?

Let's look at the Colored Square (R4C4).
Based on the trend:
- Right column (C4) has 92s in Rows 1 & 2.
- Bottom row (R4) has 94s in Cols 2 & 3.
- The intersection (R4C4) should likely have 90s, specifically 92 or 94.

Let's look at the Tangram pieces. There are 7 pieces.
If the answer is a single number, it might be the sum of the values of the pieces?
Or maybe the number hidden in the tangram?

Another possibility: The sum of the digits?
No.

Let's look at the colors.
Red, Green, Yellow, Orange, Blue, Purple.
Is there a code?
R=1, G=2...?

Let's try one more calculation.
Look at R3C3. It has 73 and 92.
Look at R2C4. It has 73 and 92.
Look at R1C4. It has 73 and 92.
Look at R4C2. It has 82 and 94.
Look at R4C3. It has 82 and 94.

The square R3C4 (Above the colored one) is missing from my analysis.
Let's find R3C4.
It is to the right of R3C3 ($27+46$ etc).
R3C4 contains:
$55+37 = 92$
$70+22 = 92$
$53+39 = 92$
$19+73 = 92$
$45+47 = 92$
$16+57$ is in R1C4.
Wait, I think I misidentified the rows earlier.
Let's look at the block with $55+37$.
It is directly above the colored square?
No, the colored square is at the bottom right.
The square directly above it contains $55+37$, $70+22$, $53+39$, $19+73$, $45+47$.
All these sums are 92.
So R3C4 is all 92s.

The square to the left of the colored one is R4C3.
It contains $50+44=94$, $26+56=82$, $65+17=82$, $19+75=94$, $35+47=82$.
So R4C3 has 82s and 94s.

The square above R4C3 is R3C3.
It contains $27+46=73$, $30+43=73$, $49+43=92$, $26+66=92$.
So R3C3 has 73s and 92s.

Now, what about R4C4 (The Colored Square)?
Neighbors:
- Above (R3C4): All 92s.
- Left (R4C3): 82s and 94s.

If we follow the pattern of the right column (C4):
R1C4: 73, 92
R2C4: 73, 92
R3C4: 92
R4C4: ?

If we follow the pattern of the bottom row (R4):
R4C1: 82
R4C2: 82, 94
R4C3: 82, 94
R4C4: ?

The numbers 82, 92, 94 are present.
82 is $80+2$.
92 is $90+2$.
94 is $90+4$.

Notice that $82 + 10 = 92$.
$92 + 2 = 94$?

Let's look at the Tangram again.
The Tangram has 7 pieces.
Is the answer 7? Unlikely given the other numbers are large.
Is the answer related to the area?
If the large square has area 16 (4x4 grid of small units?), the tangram pieces sum to 16.
But the other numbers are sums of additions.

Let's assume the question asks for the missing sums that would fit in the colored square.
Given the neighbors are 92 (above) and 82/94 (left), the colored square likely contains 92 and 94? Or just 92?

However, there is a specific property of Tangrams.
The 7 pieces can form a square.
If we assign values to the pieces based on their size relative to the whole:
- Large Triangles: 1/4 each.
- Medium Triangle: 1/8.
- Small Triangles: 1/16 each.
- Square: 1/8.
- Parallelogram: 1/8.

If the total sum of the square is X, then the pieces are fractions of X.
If the surrounding squares sum to ~92, maybe the total sum of the colored square is also 92?

Let's check if 92 fits the pattern.
R3C4 is all 92s.
R4C3 has 94s and 82s. Average is $(94+82)/2 = 88$.
R4C4 is adjacent to both.

Let's look at the diagonal from Top-Left to Bottom-Right.
R1C1: ~72
R2C2: ~73/84
R3C3: ~73/92
R4C4: ?

The sums are increasing.
72 -> 84 -> 92 -> ?

Let's look at the other diagonal.
R1C4: 73/92
R2C3: 73
R3C2: 83/84
R4C1: 82

This doesn't show a clear linear progression.

Alternative Idea:
Look at the last digit of the sums.
R3C4: All end in 2.
R4C3: End in 2 and 4.
R4C2: End in 2 and 4.
R4C1: Ends in 2.

The dominant ending digit is 2.
So the sums in the colored square likely end in 2.
Possible numbers: 92, 82, 102?
Given the range is 70-90, 92 is the strongest candidate.

Also, the square above (R3C4) is uniformly 92.
The square to the left (R4C3) is mixed.
Often, the corner square completes a symmetry.
If R3C4 is 92, and R4C3 has 94/82, maybe R4C4 is 92 to match the column?

Let's verify with the Tangram.
Does the Tangram represent the number 92?
No obvious connection.

However, in many such puzzles, if a region is colored, it might simply mean "Calculate the sum that belongs here based on the pattern".
The pattern in Column 4 is strongly 92.
R1C4 has 92s.
R2C4 has 92s.
R3C4 has 92s.
Therefore, R4C4 likely has 92.

Final Answer:
The missing number is 92.