2nd Grade Math Puzzles - Free Printable

Let’s solve the maze step by step.

We start at 0, and we must follow arrows from one hexagon to the next, applying each operation as we go. We need to end up with exactly 20 at the END hexagon.

The maze is arranged in a grid:

Row 1: START → +7 → –3 → x2
Row 2: +5 → x2 → –2 → +3
Row 3: x2 → –3 → x2 → +6
Row 4: +4 → x1 → –2 → END

Arrows point right and down only (from the diagram). So from any cell, you can go right or down — but not left or up.

We are told there are two possible routes that give us 20. Let’s find them.

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Let’s label positions for clarity:

Let’s use (row, col) starting from top-left as (1,1):

(1,1): START
(1,2): +7
(1,3): –3
(1,4): x2

(2,1): +5
(2,2): x2
(2,3): –2
(2,4): +3

(3,1): x2
(3,2): –3
(3,3): x2
(3,4): +6

(4,1): +4
(4,2): x1
(4,3): –2
(4,4): END

From START (1,1), we can go:
- Right to (1,2) [+7]
- Down to (2,1) [+5]

We’ll try paths systematically.

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Try Path 1: Start → Right → Right → Right → Down → Down → Down → Right?

Wait — let’s think in terms of moves. From START, we need to reach END at (4,4). That means we must make 3 moves right and 3 moves down in some order — total 6 moves after START.

But since the grid is 4x4, and we start at (1,1), to get to (4,4), we need exactly 3 rights and 3 downs.

Total number of paths = C(6,3) = 20 — too many to check manually. But the problem says only two routes give 20. So let’s try promising ones.

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Let’s try going down first:

Path A:
START (0)
→ Down to (2,1): +5 → total = 5
→ Down to (3,1): x2 → 5×2 = 10
→ Down to (4,1): +4 → 10+4 = 14
→ Right to (4,2): x1 → 14×1 = 14
→ Right to (4,3): –2 → 14–2 = 12
→ Right to (4,4): END → 12 ≠ 20 → too low.

Path B:
START (0)
→ Down to (2,1): +5 → 5
→ Right to (2,2): x2 → 10
→ Right to (2,3): –2 → 8
→ Right to (2,4): +3 → 11
→ Down to (3,4): +6 → 17
→ Down to (4,4): END → 17 ≠ 20.

Path C:
START (0)
→ Down to (2,1): +5 → 5
→ Right to (2,2): x2 → 10
→ Down to (3,2): –3 → 7
→ Right to (3,3): x2 → 14
→ Right to (3,4): +6 → 20
→ Down to (4,4): END → YES! 20.

That’s one route:
START → +5 → x2 → –3 → x2 → +6 → END

Let’s write the steps clearly:

0
+5 → 5
x2 → 10
–3 → 7
x2 → 14
+6 → 20
END → 20 ✔

Now let’s find the second route.

Try going right first:

Path D:
START (0)
→ Right to (1,2): +7 → 7
→ Right to (1,3): –3 → 4
→ Right to (1,4): x2 → 8
→ Down to (2,4): +3 → 11
→ Down to (3,4): +6 → 17
→ Down to (4,4): END → 17 ✘

Path E:
START (0)
→ Right to (1,2): +7 → 7
→ Down to (2,2): x2 → 14
→ Down to (3,2): –3 → 11
→ Right to (3,3): x2 → 22
→ Right to (3,4): +6 → 28
→ Down to (4,4): END → 28 ✘

Path F:
START (0)
→ Right to (1,2): +7 → 7
→ Down to (2,2): x2 → 14
→ Right to (2,3): –2 → 12
→ Right to (2,4): +3 → 15
→ Down to (3,4): +6 → 21
→ Down to (4,4): END → 21 ✘

Path G:
START (0)
→ Right to (1,2): +7 → 7
→ Down to (2,2): x2 → 14
→ Right to (2,3): –2 → 12
→ Down to (3,3): x2 → 24
→ Right to (3,4): +6 → 30
→ Down to (4,4): END → 30 ✘

Path H:
START (0)
→ Right to (1,2): +7 → 7
→ Right to (1,3): –3 → 4
→ Down to (2,3): –2 → 2
→ Right to (2,4): +3 → 5
→ Down to (3,4): +6 → 11
→ Down to (4,4): END → 11 ✘

Path I:
START (0)
→ Right to (1,2): +7 → 7
→ Right to (1,3): –3 → 4
→ Down to (2,3): –2 → 2
→ Down to (3,3): x2 → 4
→ Right to (3,4): +6 → 10
→ Down to (4,4): END → 10 ✘

Path J:
START (0)
→ Right to (1,2): +7 → 7
→ Down to (2,2): x2 → 14
→ Down to (3,2): –3 → 11
→ Down to (4,2): x1 → 11
→ Right to (4,3): –2 → 9
→ Right to (4,4): END → 9 ✘

Wait — maybe another path.

What if:

START → +7 → –3 → x2 → +3 → +6 → END? Let’s trace:

(1,1) START → (1,2) +7 → 7
→ (1,3) –3 → 4
→ (1,4) x2 → 8
→ (2,4) +3 → 11
→ (3,4) +6 → 17
→ (4,4) END → 17 ✘

Another idea:

START → +7 → x2 → –2 → x2 → +6 → END?

Trace:

(1,1) → (1,2) +7 → 7
→ (2,2) x2 → 14
→ (2,3) –2 → 12
→ (3,3) x2 → 24
→ (3,4) +6 → 30
→ (4,4) → 30 ✘

Wait — what about:

START → +5 → x2 → –2 → x2 → +6 → END?

Trace:

(1,1) → (2,1) +5 → 5
→ (2,2) x2 → 10
→ (2,3) –2 → 8
→ (3,3) x2 → 16
→ (3,4) +6 → 22
→ (4,4) → 22 ✘

Close.

What if we do:

START → +5 → x2 → –3 → x2 → +6 → END → we already did this: gives 20 ✔

Is there another?

Try:

START → +7 → –3 → x2 → –2 → x2 → +6 → END?

Trace:

(1,1) → (1,2) +7 → 7
→ (1,3) –3 → 4
→ (1,4) x2 → 8
→ (2,4) +3 → 11? Wait no — from (1,4) we can only go down to (2,4) which is +3 → 8+3=11
Then down to (3,4) +6 → 17
Then down to (4,4) → 17 ✘

Wait — what if from (1,4) we go down to (2,4) +3 → 11, then left? No, arrows only right and down.

Another possibility:

START → +7 → x2 → –3 → x2 → +6 → END?

Trace:

(1,1) → (1,2) +7 → 7
→ (2,2) x2 → 14
→ (3,2) –3 → 11
→ (3,3) x2 → 22
→ (3,4) +6 → 28
→ (4,4) → 28 ✘

Wait — perhaps:

START → +5 → +4 → x1 → –2 → END? But that’s only 4 steps — we need to reach (4,4), so must take 6 steps.

Actually, from START to END, we must pass through 6 operations (since 3 rights + 3 downs = 6 moves).

Let me try this path:

START → +7 → –3 → x2 → +3 → +6 → END? Already tried — 17.

Wait — what if:

START → +5 → x2 → –2 → +3 → +6 → END?

Trace:

(1,1) → (2,1) +5 → 5
→ (2,2) x2 → 10
→ (2,3) –2 → 8
→ (2,4) +3 → 11
→ (3,4) +6 → 17
→ (4,4) → 17 ✘

Still not 20.

Wait — let’s try:

START → +7 → x2 → –2 → –2 → x2 → +6 → END? Not possible — from (2,3) you can’t go to (3,3) then to (4,3) then to (4,4)? Let’s see:

(1,1) → (1,2) +7 → 7
→ (2,2) x2 → 14
→ (2,3) –2 → 12
→ (3,3) x2 → 24
→ (4,3) –2 → 22
→ (4,4) → 22 ✘

Hmm.

Wait — what about:

START → +5 → x2 → –3 → x2 → +6 → END → we have this: 0→5→10→7→14→20→END ✔

Now, is there a symmetric one?

Try:

START → +7 → –3 → x2 → +3 → +6 → END? 0→7→4→8→11→17→20? No, 17.

Wait — 17 + something? No.

Another idea:

START → +7 → x2 → –3 → x2 → –2 → END? Let’s see:

(1,1) → (1,2) +7 → 7
→ (2,2) x2 → 14
→ (3,2) –3 → 11
→ (3,3) x2 → 22
→ (4,3) –2 → 20
→ (4,4) → 20 ✔

Oh! This works!

Let’s write it:

0
+7 → 7
x2 → 14
–3 → 11
x2 → 22
–2 → 20
END → 20 ✔

So the second route is:
START → +7 → x2 → –3 → x2 → –2 → END

Let’s verify the positions:

(1,1) START
→ (1,2) +7
→ (2,2) x2
→ (3,2) –3
→ (3,3) x2
→ (4,3) –2
→ (4,4) END

Yes, all moves are right or down. Perfect.

So the two routes are:

Route 1:
START → +5 → x2 → –3 → x2 → +6 → END
Calculation: 0 +5 =5; 5×2=10; 10–3=7; 7×2=14; 14+6=20

Route 2:
START → +7 → x2 → –3 → x2 → –2 → END
Calculation: 0 +7=7; 7×2=14; 14–3=11; 11×2=22; 22–2=20

Both give 20.

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Final Answer:
The two possible routes are:
1. START → +5 → x2 → –3 → x2 → +6 → END
2. START → +7 → x2 → –3 → x2 → –2 → END