Puzzle game for children. Count to 100. Preschool printable ... - Free Printable
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Step-by-step solution for: Puzzle game for children. Count to 100. Preschool printable ...
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Show Answer Key & Explanations
Step-by-step solution for: Puzzle game for children. Count to 100. Preschool printable ...
To solve this puzzle, we need to find a continuous path of numbers starting at 1 and ending at 100. The rule is that each number in the path must be exactly 1 more than the previous number (e.g., 1, then 2, then 3...). We can only move to circles that are touching horizontally, vertically, or diagonally.
Let's trace the path step-by-step:
1. Start at 1 (Top left corner).
2. Look for 2: It is directly to the right of 1.
3. Look for 3: It is directly to the right of 2.
4. Look for 4: It is directly below 1.
5. Look for 5: It is directly below 4.
6. Look for 6: It is directly below 5.
7. Look for 7: It is to the right of 6.
8. Look for 8: It is to the right of 7.
9. Look for 9: It is below the 8 in the 4th row (Row 4 has two 8s; we take the one connected to 7). Wait, let's look closer. Row 4 is `6, 7, 8, 11...`. Below 7 is `10`. Below 8 is `8`. This seems tricky. Let's re-evaluate the local area.
* Row 3: `5, 8, 13...`
* Row 4: `6, 7, 8, 11...`
* Row 5: `11, 10, 9, 10...`
* Path so far: 1 -> 2 -> 3.
* From 3, where is 4? Below 1 is 4. So 3 cannot go to 4 directly because they aren't touching. Let's re-read the grid.
* Ah, 1 is at (Row 1, Col 1). 2 is at (Row 1, Col 2). 3 is at (Row 1, Col 3).
* Where is 4? It is at (Row 2, Col 1). It touches 1. But we are at 3. Does 3 touch 4? No.
* Let's check if there is another path. Maybe I missed a connection.
* Let's look at the neighbors of 3. Neighbors are 2, 16, 14, 15. None are 4.
* Let's look at the neighbors of 1. Neighbors are 2, 4, 3.
* Is it possible the path goes 1 -> 4 -> ...?
* If we go 1 -> 4, then we need 5. 5 is below 4.
* Then 6 below 5.
* Then 7 right of 6.
* Then 8 right of 7.
* Then 9? Below the first 8 (Row 3, Col 2) is 7. Below the second 8 (Row 4, Col 3) is 9 (Row 5, Col 3). Yes!
* So the path starts: 1 -> 4 -> 5 -> 6 -> 7 -> 8 -> 9.
* Let's verify the start again. The prompt says "Color the path from 1-100". Usually, these puzzles are contiguous.
* Let's check if 1 connects to 2. Yes. Does 2 connect to 3? Yes. Does 3 connect to 4? No.
* Does 1 connect to 4? Yes.
* So, does the path go through 2 and 3? If it goes 1->2->3, it gets stuck because 3 doesn't touch 4. Therefore, the path must ignore 2 and 3? That would mean 2 and 3 are not part of the solution path. This is common in these "find the hidden path" puzzles where distractors exist.
* Let's assume the path is 1 -> 4.
Let's trace forward from 9:
* Current position: 9 (Row 5, Col 3).
* Next is 10. Neighbors of 9 are: 8 (above), 11 (left), 10 (right), 48 (below right? no, let's check coords).
* Row 5: `11, 10, 9, 10, 23...`
* To the right of 9 is 10.
* Next is 11. To the right of 10 is 23? No. Above 10 (Row 4, Col 4) is 11. Yes.
* So: 9 -> 10 -> 11.
* Next is 12. Neighbors of 11 (Row 4, Col 4):
* Above: 15 (Row 3, Col 4).
* Left: 8 (Row 4, Col 3).
* Right: 22 (Row 4, Col 5).
* Below: 10 (Row 5, Col 4).
* Diagonals: 13 (Row 3, Col 3), 20 (Row 3, Col 5), 48 (Row 6, Col 3?? No Row 6 is `52...`). Let's check Row 3/4/5 carefully.
* Row 3: `5, 8, 13, 12, 13, 20...`
* Row 4: `6, 7, 8, 11, 22, 21...`
* Row 5: `11, 10, 9, 10, 23, 24...`
* We are at 11 (Row 4, Col 4).
* Where is 12? It is at Row 3, Col 4. It is directly above 11.
* So: 11 -> 12.
* Next is 13. Neighbors of 12 (Row 3, Col 4):
* Left: 13 (Row 3, Col 3).
* Right: 13 (Row 3, Col 5).
* Let's pick the one that leads to 14.
* If we go Left to 13 (Row 3, Col 3): Neighbors are 8, 14, 11, 13, 22. 14 is at Row 2, Col 3. Yes, 13 (R3C3) touches 14 (R2C3).
* If we go Right to 13 (Row 3, Col 5): Neighbors are 12, 20, 21, 22, 13(R3C4). No 14 nearby.
* So we go Left. 12 -> 13 (the left one).
* Next is 14. Above 13 (R3C3) is 14 (R2C3).
* So: 13 -> 14.
* Next is 15. Right of 14 is 15 (R2C4).
* So: 14 -> 15.
* Next is 16. Left of 15 is 14. Above 15 is 3? No (R1C4 is 16? No, R1 is `1,2,3,16...`).
* Row 1: `1, 2, 3, 16, 17...`
* Row 2: `4, 3, 14, 15...`
* 15 is at R2C4. Above it is R1C4 which is 16.
* So: 15 -> 16.
* Next is 17. Right of 16 is 17 (R1C5).
* So: 16 -> 17.
* Next is 18. Below 17 is 18 (R2C5).
* So: 17 -> 18.
* Next is 19. Right of 18 is 19 (R2C6).
* So: 18 -> 19.
* Next is 20. Below 19 is 20 (R3C6). Note: There is also a 20 at R1C6 and R3C6. We are at R2C6. Below is R3C6 which is 20.
* So: 19 -> 20.
* Next is 21. Right of 20 (R3C6) is 29? No. Below is 24? No.
* Let's check neighbors of 20 (R3C6).
* Up: 19. Left: 13. Right: 29. Down: 24 (R4C6 is 21? No, R4 is `...22, 21, 26...`). R4C6 is 21.
* So below 20 is 21.
* So: 20 -> 21.
* Next is 22. Left of 21 (R4C6) is 22 (R4C5).
* So: 21 -> 22.
* Next is 23. Below 22 is 23 (R5C5).
* So: 22 -> 23.
* Next is 24. Right of 23 is 24 (R5C6).
* So: 23 -> 24.
* Next is 25. Right of 24 is 25 (R5C7).
* So: 24 -> 25.
* Next is 26. Above 25 is 29? No. Right is 40? No.
* Neighbors of 25 (R5C7): Up is 29 (R4C7). Down is 98? No (R6C7 is 98? No, R6 is `52...97,98`). R6C7 is 98.
* Left is 24.
* Diagonal Up-Right: 37? No.
* Let's re-examine the grid around 25.
* Row 4: `...21, 26, 27, 36` (Cols 6,7,8,9). Wait, R4C7 is 26?
* Let's re-read Row 4 carefully: `6, 7, 8, 11, 22, 21, 26, 27, 36`.
* Col 6 is 21. Col 7 is 26.
* Row 5: `11, 10, 9, 10, 23, 24, 25, 40, 37`.
* Col 6 is 24. Col 7 is 25.
* So 25 is at R5C7.
* Where is 26? It is at R4C7. It is directly above 25.
* So: 25 -> 26.
* Next is 27. Right of 26 is 27 (R4C8).
* So: 26 -> 27.
* Next is 28. Above 27 is 31? No. Right is 36? No.
* Neighbors of 27 (R4C8):
* Up: 31 (R3C8 is 28? Let's check Row 3).
* Row 3: `5, 8, 13, 12, 13, 20, 29, 28, 35`.
* Col 8 is 28.
* So above 27 (R4C8) is 28 (R3C8).
* So: 27 -> 28.
* Next is 29. Left of 28 is 29 (R3C7).
* So: 28 -> 29.
* Next is 30. Above 29 is 30 (R2C7).
* So: 29 -> 30.
* Next is 31. Right of 30 is 31 (R2C8).
* So: 30 -> 31.
* Next is 32. Above 31 is 32 (R1C8).
* So: 31 -> 32.
* Next is 33. Right of 32 is 33 (R1C9).
* So: 32 -> 33.
* Next is 34. Below 33 is 34 (R2C9).
* So: 33 -> 34.
* Next is 35. Below 34 is 35 (R3C9).
* So: 34 -> 35.
* Next is 36. Below 35 is 36 (R4C9).
* So: 35 -> 36.
* Next is 37. Below 36 is 37 (R5C9).
* So: 36 -> 37.
* Next is 38. Below 37 is 38 (R6C9).
* Row 6: `50, 49, 48, 47, 44, 43, 42, 39, 38`.
* Yes, R6C9 is 38.
* So: 37 -> 38.
* Next is 39. Left of 38 is 39 (R6C8).
* So: 38 -> 39.
* Next is 40. Left of 39 is 40 (R6C7).
* So: 39 -> 40.
* Next is 41. Below 40 is 41 (R7C8? No, R7 is `51...41`).
* Row 7: `51, 54, 55, 46, 45, 42, 41, 40, 41`.
* We are at 40 (R6C7).
* Neighbors of 40 (R6C7):
* Left: 42. Right: 39. Up: 25. Down: 41 (R7C7).
* So below is 41 (R7C7).
* So: 40 -> 41.
* Next is 42. Left of 41 (R7C7) is 42 (R7C6).
* So: 41 -> 42.
* Next is 43. Above 42 is 43 (R6C6).
* So: 42 -> 43.
* Next is 44. Left of 43 is 44 (R6C5).
* So: 43 -> 44.
* Next is 45. Below 44 is 45 (R7C5).
* So: 44 -> 45.
* Next is 46. Left of 45 is 46 (R7C4).
* So: 45 -> 46.
* Next is 47. Above 46 is 47 (R6C4).
* So: 46 -> 47.
* Next is 48. Left of 47 is 48 (R6C3).
* So: 47 -> 48.
* Next is 49. Left of 48 is 49 (R6C2).
* So: 48 -> 49.
* Next is 50. Left of 49 is 50 (R6C1).
* So: 49 -> 50.
* Next is 51. Below 50 is 51 (R7C1).
* So: 50 -> 51.
* Next is 52. Below 51 is 52 (R8C1).
* Row 8: `52, 53, 58, 57, 58, 97, 98, 99, 100`.
* So: 51 -> 52.
* Next is 53. Right of 52 is 53 (R8C2).
* So: 52 -> 53.
* Next is 54. Above 53 is 54 (R7C2).
* So: 53 -> 54.
* Next is 55. Right of 54 is 55 (R7C3).
* So: 54 -> 55.
* Next is 56. Below 55 is 56 (R8C3 is 58? No).
* Let's check Row 8 again: `52, 53, 58, 57...`
* R8C3 is 58.
* Where is 56?
* Row 9: `71, 54, 55, 56, 59...`
* R9C4 is 56.
* We are at 55 (R7C3).
* Neighbors of 55 (R7C3):
* Left: 54. Right: 46. Up: 55 (R6C3 is 48? No R6C3 is 48. R7C3 is 55. Up is R6C3=48. Down is R8C3=58).
* Diagonal Down-Right: R8C4 is 57.
* Diagonal Down-Left: R8C2 is 53.
* This path seems blocked. Let's re-trace back to 53/54/55.
Let's look at the area around 50-60 again.
Row 6: `50, 49, 48, 47, 44, 43, 42, 39, 38`
Row 7: `51, 54, 55, 46, 45, 42, 41, 40, 41`
Row 8: `52, 53, 58, 57, 58, 97, 98, 99, 100`
Row 9: `71, 54, 55, 56, 59, 96, 95, 94, 95`
We arrived at 53 (R8C2).
Next is 54.
Options for 54:
- R7C2 is 54. Touches 53 (R8C2) vertically.
- R9C2 is 54. Touches 53 (R8C2) vertically.
If we go to R7C2 (54):
Next is 55. Right is R7C3 (55).
Next is 56. Neighbors of R7C3 (55):
- Down is R8C3 (58).
- Down-Right is R8C4 (57).
- Right is R7C4 (46).
- Up is R6C3 (48).
- There is no 56 touching R7C3.
So, going to R7C2 was a dead end.
Let's try the other 54: R9C2.
From 53 (R8C2), go down to 54 (R9C2).
Next is 55. Right of R9C2 is 55 (R9C3).
Next is 56. Right of R9C3 is 56 (R9C4).
Next is 57. Above 56 (R9C4) is 57 (R8C4).
Next is 58. Left of 57 (R8C4) is 58 (R8C3).
Next is 59. Right of 57 (R8C4) is 58 (R8C5). Wait, we need 59.
Let's check neighbors of 58 (R8C3).
- Up: R7C3 is 55.
- Left: R8C2 is 53.
- Down: R9C3 is 55.
- Right: R8C4 is 57.
This is a loop 54-55-56-57-58. Where is 59?
R9C5 is 59.
Does 58 touch 59?
R8C3 (58) does not touch R9C5 (59).
R8C5 is 58. Does R8C5 touch R9C5 (59)? Yes, vertically.
So, we need to get to 58 at R8C5.
Let's re-trace from 56.
We were at 56 (R9C4).
Next is 57.
Options for 57:
- R8C4 is 57. (Above 56).
- Are there other 57s? No.
So we must go 56 -> 57 (R8C4).
Next is 58.
Options for 58 touching R8C4:
- Left: R8C3 is 58.
- Right: R8C5 is 58.
If we go Left to R8C3 (58):
Next is 59. Neighbors of R8C3: 53, 55, 57. No 59. Dead end.
If we go Right to R8C5 (58):
Next is 59. Neighbor of R8C5:
- Down: R9C5 is 59.
So: 58 (R8C5) -> 59.
Okay, so the path segment is:
... -> 53 (R8C2) -> 54 (R9C2) -> 55 (R9C3) -> 56 (R9C4) -> 57 (R8C4) -> 58 (R8C5) -> 59 (R9C5).
Let's continue from 59 (R9C5).
Next is 60.
Neighbors of 59 (R9C5):
- Up: R8C5 is 58.
- Left: R9C4 is 56.
- Right: R9C6 is 96.
- Down: R10C5 is 60? Let's check Row 10.
Row 10: `70, 69, 62, 61, 60, 83, 84, 93, 92`.
R10C5 is 60.
So: 59 -> 60.
Next is 61. Left of 60 (R10C5) is 61 (R10C4).
So: 60 -> 61.
Next is 62. Left of 61 is 62 (R10C3).
So: 61 -> 62.
Next is 63. Below 62 is 63 (R11C3).
Row 11: `71, 68, 63, 64, 81, 82, 85, 86, 91`.
So: 62 -> 63.
Next is 64. Right of 63 is 64 (R11C4).
So: 63 -> 64.
Next is 65. Below 64 is 65 (R12C4).
Row 12: `72, 67, 66, 65, 80, 79, 80, 87, 90`.
So: 64 -> 65.
Next is 66. Left of 65 is 66 (R12C3).
So: 65 -> 66.
Next is 67. Left of 66 is 67 (R12C2).
So: 66 -> 67.
Next is 68. Above 67 is 68 (R11C2).
So: 67 -> 68.
Next is 69. Above 68 is 69 (R10C2).
So: 68 -> 69.
Next is 70. Left of 69 is 70 (R10C1).
So: 69 -> 70.
Next is 71. Below 70 is 71 (R11C1).
So: 70 -> 71.
Next is 72. Below 71 is 72 (R12C1).
So: 71 -> 72.
Next is 73. Below 72 is 73 (R13C1).
Row 13: `73, 74, 75, 76, 77, 78, 81, 88, 89`.
So: 72 -> 73.
Next is 74. Right of 73 is 74 (R13C2).
So: 73 -> 74.
Next is 75. Right of 74 is 75 (R13C3).
So: 74 -> 75.
Next is 76. Right of 75 is 76 (R13C4).
So: 75 -> 76.
Next is 77. Right of 76 is 77 (R13C5).
So: 76 -> 77.
Next is 78. Right of 77 is 78 (R13C6).
So: 77 -> 78.
Next is 79. Above 78 is 79 (R12C6).
So: 78 -> 79.
Next is 80. Left of 79 is 80 (R12C5).
So: 79 -> 80.
Next is 81. Above 80 is 81 (R11C5).
So: 80 -> 81.
Next is 82. Right of 81 is 82 (R11C6).
So: 81 -> 82.
Next is 83. Above 82 is 83 (R10C6).
So: 82 -> 83.
Next is 84. Right of 83 is 84 (R10C7).
So: 83 -> 84.
Next is 85. Below 84 is 85 (R11C7).
So: 84 -> 85.
Next is 86. Right of 85 is 86 (R11C8).
So: 85 -> 86.
Next is 87. Below 86 is 87 (R12C8).
So: 86 -> 87.
Next is 88. Below 87 is 88 (R13C8).
So: 87 -> 88.
Next is 89. Right of 88 is 89 (R13C9).
So: 88 -> 89.
Next is 90. Above 89 is 90 (R12C9).
So: 89 -> 90.
Next is 91. Above 90 is 91 (R11C9).
So: 90 -> 91.
Next is 92. Above 91 is 92 (R10C9).
So: 91 -> 92.
Next is 93. Left of 92 is 93 (R10C8).
So: 92 -> 93.
Next is 94. Below 93 is 94 (R9C8).
Row 9: `...96, 95, 94, 95`. R9C8 is 94.
So: 93 -> 94.
Next is 95. Left of 94 is 95 (R9C7).
So: 94 -> 95.
Next is 96. Left of 95 is 96 (R9C6).
So: 95 -> 96.
Next is 97. Above 96 is 97 (R8C6).
Row 8: `...58, 97, 98, 99, 100`. R8C6 is 97.
So: 96 -> 97.
Next is 98. Right of 97 is 98 (R8C7).
So: 97 -> 98.
Next is 99. Right of 98 is 99 (R8C8).
So: 98 -> 99.
Next is 100. Right of 99 is 100 (R8C9).
So: 99 -> 100.
The path is complete and valid.
Final Answer:
The path follows this sequence of coordinates (Row, Column):
(1,1)→(2,1)→(3,1)→(4,1)→(5,1) is WRONG. My manual trace started 1->4.
Let's list the numbers in order to be absolutely sure for the final output.
1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100.
Let's trace the path step-by-step:
1. Start at 1 (Top left corner).
2. Look for 2: It is directly to the right of 1.
3. Look for 3: It is directly to the right of 2.
4. Look for 4: It is directly below 1.
5. Look for 5: It is directly below 4.
6. Look for 6: It is directly below 5.
7. Look for 7: It is to the right of 6.
8. Look for 8: It is to the right of 7.
9. Look for 9: It is below the 8 in the 4th row (Row 4 has two 8s; we take the one connected to 7). Wait, let's look closer. Row 4 is `6, 7, 8, 11...`. Below 7 is `10`. Below 8 is `8`. This seems tricky. Let's re-evaluate the local area.
* Row 3: `5, 8, 13...`
* Row 4: `6, 7, 8, 11...`
* Row 5: `11, 10, 9, 10...`
* Path so far: 1 -> 2 -> 3.
* From 3, where is 4? Below 1 is 4. So 3 cannot go to 4 directly because they aren't touching. Let's re-read the grid.
* Ah, 1 is at (Row 1, Col 1). 2 is at (Row 1, Col 2). 3 is at (Row 1, Col 3).
* Where is 4? It is at (Row 2, Col 1). It touches 1. But we are at 3. Does 3 touch 4? No.
* Let's check if there is another path. Maybe I missed a connection.
* Let's look at the neighbors of 3. Neighbors are 2, 16, 14, 15. None are 4.
* Let's look at the neighbors of 1. Neighbors are 2, 4, 3.
* Is it possible the path goes 1 -> 4 -> ...?
* If we go 1 -> 4, then we need 5. 5 is below 4.
* Then 6 below 5.
* Then 7 right of 6.
* Then 8 right of 7.
* Then 9? Below the first 8 (Row 3, Col 2) is 7. Below the second 8 (Row 4, Col 3) is 9 (Row 5, Col 3). Yes!
* So the path starts: 1 -> 4 -> 5 -> 6 -> 7 -> 8 -> 9.
* Let's verify the start again. The prompt says "Color the path from 1-100". Usually, these puzzles are contiguous.
* Let's check if 1 connects to 2. Yes. Does 2 connect to 3? Yes. Does 3 connect to 4? No.
* Does 1 connect to 4? Yes.
* So, does the path go through 2 and 3? If it goes 1->2->3, it gets stuck because 3 doesn't touch 4. Therefore, the path must ignore 2 and 3? That would mean 2 and 3 are not part of the solution path. This is common in these "find the hidden path" puzzles where distractors exist.
* Let's assume the path is 1 -> 4.
Let's trace forward from 9:
* Current position: 9 (Row 5, Col 3).
* Next is 10. Neighbors of 9 are: 8 (above), 11 (left), 10 (right), 48 (below right? no, let's check coords).
* Row 5: `11, 10, 9, 10, 23...`
* To the right of 9 is 10.
* Next is 11. To the right of 10 is 23? No. Above 10 (Row 4, Col 4) is 11. Yes.
* So: 9 -> 10 -> 11.
* Next is 12. Neighbors of 11 (Row 4, Col 4):
* Above: 15 (Row 3, Col 4).
* Left: 8 (Row 4, Col 3).
* Right: 22 (Row 4, Col 5).
* Below: 10 (Row 5, Col 4).
* Diagonals: 13 (Row 3, Col 3), 20 (Row 3, Col 5), 48 (Row 6, Col 3?? No Row 6 is `52...`). Let's check Row 3/4/5 carefully.
* Row 3: `5, 8, 13, 12, 13, 20...`
* Row 4: `6, 7, 8, 11, 22, 21...`
* Row 5: `11, 10, 9, 10, 23, 24...`
* We are at 11 (Row 4, Col 4).
* Where is 12? It is at Row 3, Col 4. It is directly above 11.
* So: 11 -> 12.
* Next is 13. Neighbors of 12 (Row 3, Col 4):
* Left: 13 (Row 3, Col 3).
* Right: 13 (Row 3, Col 5).
* Let's pick the one that leads to 14.
* If we go Left to 13 (Row 3, Col 3): Neighbors are 8, 14, 11, 13, 22. 14 is at Row 2, Col 3. Yes, 13 (R3C3) touches 14 (R2C3).
* If we go Right to 13 (Row 3, Col 5): Neighbors are 12, 20, 21, 22, 13(R3C4). No 14 nearby.
* So we go Left. 12 -> 13 (the left one).
* Next is 14. Above 13 (R3C3) is 14 (R2C3).
* So: 13 -> 14.
* Next is 15. Right of 14 is 15 (R2C4).
* So: 14 -> 15.
* Next is 16. Left of 15 is 14. Above 15 is 3? No (R1C4 is 16? No, R1 is `1,2,3,16...`).
* Row 1: `1, 2, 3, 16, 17...`
* Row 2: `4, 3, 14, 15...`
* 15 is at R2C4. Above it is R1C4 which is 16.
* So: 15 -> 16.
* Next is 17. Right of 16 is 17 (R1C5).
* So: 16 -> 17.
* Next is 18. Below 17 is 18 (R2C5).
* So: 17 -> 18.
* Next is 19. Right of 18 is 19 (R2C6).
* So: 18 -> 19.
* Next is 20. Below 19 is 20 (R3C6). Note: There is also a 20 at R1C6 and R3C6. We are at R2C6. Below is R3C6 which is 20.
* So: 19 -> 20.
* Next is 21. Right of 20 (R3C6) is 29? No. Below is 24? No.
* Let's check neighbors of 20 (R3C6).
* Up: 19. Left: 13. Right: 29. Down: 24 (R4C6 is 21? No, R4 is `...22, 21, 26...`). R4C6 is 21.
* So below 20 is 21.
* So: 20 -> 21.
* Next is 22. Left of 21 (R4C6) is 22 (R4C5).
* So: 21 -> 22.
* Next is 23. Below 22 is 23 (R5C5).
* So: 22 -> 23.
* Next is 24. Right of 23 is 24 (R5C6).
* So: 23 -> 24.
* Next is 25. Right of 24 is 25 (R5C7).
* So: 24 -> 25.
* Next is 26. Above 25 is 29? No. Right is 40? No.
* Neighbors of 25 (R5C7): Up is 29 (R4C7). Down is 98? No (R6C7 is 98? No, R6 is `52...97,98`). R6C7 is 98.
* Left is 24.
* Diagonal Up-Right: 37? No.
* Let's re-examine the grid around 25.
* Row 4: `...21, 26, 27, 36` (Cols 6,7,8,9). Wait, R4C7 is 26?
* Let's re-read Row 4 carefully: `6, 7, 8, 11, 22, 21, 26, 27, 36`.
* Col 6 is 21. Col 7 is 26.
* Row 5: `11, 10, 9, 10, 23, 24, 25, 40, 37`.
* Col 6 is 24. Col 7 is 25.
* So 25 is at R5C7.
* Where is 26? It is at R4C7. It is directly above 25.
* So: 25 -> 26.
* Next is 27. Right of 26 is 27 (R4C8).
* So: 26 -> 27.
* Next is 28. Above 27 is 31? No. Right is 36? No.
* Neighbors of 27 (R4C8):
* Up: 31 (R3C8 is 28? Let's check Row 3).
* Row 3: `5, 8, 13, 12, 13, 20, 29, 28, 35`.
* Col 8 is 28.
* So above 27 (R4C8) is 28 (R3C8).
* So: 27 -> 28.
* Next is 29. Left of 28 is 29 (R3C7).
* So: 28 -> 29.
* Next is 30. Above 29 is 30 (R2C7).
* So: 29 -> 30.
* Next is 31. Right of 30 is 31 (R2C8).
* So: 30 -> 31.
* Next is 32. Above 31 is 32 (R1C8).
* So: 31 -> 32.
* Next is 33. Right of 32 is 33 (R1C9).
* So: 32 -> 33.
* Next is 34. Below 33 is 34 (R2C9).
* So: 33 -> 34.
* Next is 35. Below 34 is 35 (R3C9).
* So: 34 -> 35.
* Next is 36. Below 35 is 36 (R4C9).
* So: 35 -> 36.
* Next is 37. Below 36 is 37 (R5C9).
* So: 36 -> 37.
* Next is 38. Below 37 is 38 (R6C9).
* Row 6: `50, 49, 48, 47, 44, 43, 42, 39, 38`.
* Yes, R6C9 is 38.
* So: 37 -> 38.
* Next is 39. Left of 38 is 39 (R6C8).
* So: 38 -> 39.
* Next is 40. Left of 39 is 40 (R6C7).
* So: 39 -> 40.
* Next is 41. Below 40 is 41 (R7C8? No, R7 is `51...41`).
* Row 7: `51, 54, 55, 46, 45, 42, 41, 40, 41`.
* We are at 40 (R6C7).
* Neighbors of 40 (R6C7):
* Left: 42. Right: 39. Up: 25. Down: 41 (R7C7).
* So below is 41 (R7C7).
* So: 40 -> 41.
* Next is 42. Left of 41 (R7C7) is 42 (R7C6).
* So: 41 -> 42.
* Next is 43. Above 42 is 43 (R6C6).
* So: 42 -> 43.
* Next is 44. Left of 43 is 44 (R6C5).
* So: 43 -> 44.
* Next is 45. Below 44 is 45 (R7C5).
* So: 44 -> 45.
* Next is 46. Left of 45 is 46 (R7C4).
* So: 45 -> 46.
* Next is 47. Above 46 is 47 (R6C4).
* So: 46 -> 47.
* Next is 48. Left of 47 is 48 (R6C3).
* So: 47 -> 48.
* Next is 49. Left of 48 is 49 (R6C2).
* So: 48 -> 49.
* Next is 50. Left of 49 is 50 (R6C1).
* So: 49 -> 50.
* Next is 51. Below 50 is 51 (R7C1).
* So: 50 -> 51.
* Next is 52. Below 51 is 52 (R8C1).
* Row 8: `52, 53, 58, 57, 58, 97, 98, 99, 100`.
* So: 51 -> 52.
* Next is 53. Right of 52 is 53 (R8C2).
* So: 52 -> 53.
* Next is 54. Above 53 is 54 (R7C2).
* So: 53 -> 54.
* Next is 55. Right of 54 is 55 (R7C3).
* So: 54 -> 55.
* Next is 56. Below 55 is 56 (R8C3 is 58? No).
* Let's check Row 8 again: `52, 53, 58, 57...`
* R8C3 is 58.
* Where is 56?
* Row 9: `71, 54, 55, 56, 59...`
* R9C4 is 56.
* We are at 55 (R7C3).
* Neighbors of 55 (R7C3):
* Left: 54. Right: 46. Up: 55 (R6C3 is 48? No R6C3 is 48. R7C3 is 55. Up is R6C3=48. Down is R8C3=58).
* Diagonal Down-Right: R8C4 is 57.
* Diagonal Down-Left: R8C2 is 53.
* This path seems blocked. Let's re-trace back to 53/54/55.
Let's look at the area around 50-60 again.
Row 6: `50, 49, 48, 47, 44, 43, 42, 39, 38`
Row 7: `51, 54, 55, 46, 45, 42, 41, 40, 41`
Row 8: `52, 53, 58, 57, 58, 97, 98, 99, 100`
Row 9: `71, 54, 55, 56, 59, 96, 95, 94, 95`
We arrived at 53 (R8C2).
Next is 54.
Options for 54:
- R7C2 is 54. Touches 53 (R8C2) vertically.
- R9C2 is 54. Touches 53 (R8C2) vertically.
If we go to R7C2 (54):
Next is 55. Right is R7C3 (55).
Next is 56. Neighbors of R7C3 (55):
- Down is R8C3 (58).
- Down-Right is R8C4 (57).
- Right is R7C4 (46).
- Up is R6C3 (48).
- There is no 56 touching R7C3.
So, going to R7C2 was a dead end.
Let's try the other 54: R9C2.
From 53 (R8C2), go down to 54 (R9C2).
Next is 55. Right of R9C2 is 55 (R9C3).
Next is 56. Right of R9C3 is 56 (R9C4).
Next is 57. Above 56 (R9C4) is 57 (R8C4).
Next is 58. Left of 57 (R8C4) is 58 (R8C3).
Next is 59. Right of 57 (R8C4) is 58 (R8C5). Wait, we need 59.
Let's check neighbors of 58 (R8C3).
- Up: R7C3 is 55.
- Left: R8C2 is 53.
- Down: R9C3 is 55.
- Right: R8C4 is 57.
This is a loop 54-55-56-57-58. Where is 59?
R9C5 is 59.
Does 58 touch 59?
R8C3 (58) does not touch R9C5 (59).
R8C5 is 58. Does R8C5 touch R9C5 (59)? Yes, vertically.
So, we need to get to 58 at R8C5.
Let's re-trace from 56.
We were at 56 (R9C4).
Next is 57.
Options for 57:
- R8C4 is 57. (Above 56).
- Are there other 57s? No.
So we must go 56 -> 57 (R8C4).
Next is 58.
Options for 58 touching R8C4:
- Left: R8C3 is 58.
- Right: R8C5 is 58.
If we go Left to R8C3 (58):
Next is 59. Neighbors of R8C3: 53, 55, 57. No 59. Dead end.
If we go Right to R8C5 (58):
Next is 59. Neighbor of R8C5:
- Down: R9C5 is 59.
So: 58 (R8C5) -> 59.
Okay, so the path segment is:
... -> 53 (R8C2) -> 54 (R9C2) -> 55 (R9C3) -> 56 (R9C4) -> 57 (R8C4) -> 58 (R8C5) -> 59 (R9C5).
Let's continue from 59 (R9C5).
Next is 60.
Neighbors of 59 (R9C5):
- Up: R8C5 is 58.
- Left: R9C4 is 56.
- Right: R9C6 is 96.
- Down: R10C5 is 60? Let's check Row 10.
Row 10: `70, 69, 62, 61, 60, 83, 84, 93, 92`.
R10C5 is 60.
So: 59 -> 60.
Next is 61. Left of 60 (R10C5) is 61 (R10C4).
So: 60 -> 61.
Next is 62. Left of 61 is 62 (R10C3).
So: 61 -> 62.
Next is 63. Below 62 is 63 (R11C3).
Row 11: `71, 68, 63, 64, 81, 82, 85, 86, 91`.
So: 62 -> 63.
Next is 64. Right of 63 is 64 (R11C4).
So: 63 -> 64.
Next is 65. Below 64 is 65 (R12C4).
Row 12: `72, 67, 66, 65, 80, 79, 80, 87, 90`.
So: 64 -> 65.
Next is 66. Left of 65 is 66 (R12C3).
So: 65 -> 66.
Next is 67. Left of 66 is 67 (R12C2).
So: 66 -> 67.
Next is 68. Above 67 is 68 (R11C2).
So: 67 -> 68.
Next is 69. Above 68 is 69 (R10C2).
So: 68 -> 69.
Next is 70. Left of 69 is 70 (R10C1).
So: 69 -> 70.
Next is 71. Below 70 is 71 (R11C1).
So: 70 -> 71.
Next is 72. Below 71 is 72 (R12C1).
So: 71 -> 72.
Next is 73. Below 72 is 73 (R13C1).
Row 13: `73, 74, 75, 76, 77, 78, 81, 88, 89`.
So: 72 -> 73.
Next is 74. Right of 73 is 74 (R13C2).
So: 73 -> 74.
Next is 75. Right of 74 is 75 (R13C3).
So: 74 -> 75.
Next is 76. Right of 75 is 76 (R13C4).
So: 75 -> 76.
Next is 77. Right of 76 is 77 (R13C5).
So: 76 -> 77.
Next is 78. Right of 77 is 78 (R13C6).
So: 77 -> 78.
Next is 79. Above 78 is 79 (R12C6).
So: 78 -> 79.
Next is 80. Left of 79 is 80 (R12C5).
So: 79 -> 80.
Next is 81. Above 80 is 81 (R11C5).
So: 80 -> 81.
Next is 82. Right of 81 is 82 (R11C6).
So: 81 -> 82.
Next is 83. Above 82 is 83 (R10C6).
So: 82 -> 83.
Next is 84. Right of 83 is 84 (R10C7).
So: 83 -> 84.
Next is 85. Below 84 is 85 (R11C7).
So: 84 -> 85.
Next is 86. Right of 85 is 86 (R11C8).
So: 85 -> 86.
Next is 87. Below 86 is 87 (R12C8).
So: 86 -> 87.
Next is 88. Below 87 is 88 (R13C8).
So: 87 -> 88.
Next is 89. Right of 88 is 89 (R13C9).
So: 88 -> 89.
Next is 90. Above 89 is 90 (R12C9).
So: 89 -> 90.
Next is 91. Above 90 is 91 (R11C9).
So: 90 -> 91.
Next is 92. Above 91 is 92 (R10C9).
So: 91 -> 92.
Next is 93. Left of 92 is 93 (R10C8).
So: 92 -> 93.
Next is 94. Below 93 is 94 (R9C8).
Row 9: `...96, 95, 94, 95`. R9C8 is 94.
So: 93 -> 94.
Next is 95. Left of 94 is 95 (R9C7).
So: 94 -> 95.
Next is 96. Left of 95 is 96 (R9C6).
So: 95 -> 96.
Next is 97. Above 96 is 97 (R8C6).
Row 8: `...58, 97, 98, 99, 100`. R8C6 is 97.
So: 96 -> 97.
Next is 98. Right of 97 is 98 (R8C7).
So: 97 -> 98.
Next is 99. Right of 98 is 99 (R8C8).
So: 98 -> 99.
Next is 100. Right of 99 is 100 (R8C9).
So: 99 -> 100.
The path is complete and valid.
Final Answer:
The path follows this sequence of coordinates (Row, Column):
(1,1)→(2,1)→(3,1)→(4,1)→(5,1) is WRONG. My manual trace started 1->4.
Let's list the numbers in order to be absolutely sure for the final output.
1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100.
Parent Tip: Review the logic above to help your child master the concept of free printable iq tests.
