Another Peek Beyond the Point | A

Question 2

Try solving the following Hidato puzzles.

Question diagram 1
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Solution
Understand the Question
  • In a standard Hidato puzzle, all empty cells in a grid are filled with consecutive numbers from 11 to NN, where NN is the total number of cells in the grid.
  • Consecutive numbers must connect horizontally, vertically, or diagonally into adjacent cells.
  • If any given number printed in the grid is greater than the total number of cells NN, the puzzle violates standard Hidato rules and cannot be solved.

(i) Solve Puzzle 1.

Step 1 · Count Cells and Compare Given Values

Diagram 1

Total number of cells in the 4×44 \times 4 grid:

=4×4=16\begin{aligned} &= 4 \times 4 \\ &= 16 \end{aligned}
  • A valid Hidato puzzle of 1616 cells must only contain numbers from 11 to 1616.
  • The given numbers in the puzzle are: 1,4,8,9,14,15,20,251, 4, 8, 9, 14, 15, 20, 25.
  • The numbers 2020 and 2525 are greater than the total number of cells (1616).
Answer

(i) Puzzle 1 cannot be solved as a standard Hidato puzzle.

(ii) Solve Puzzle 2.

Step 1 · Count Cells and Compare Given Values

Count the number of cells in each row:

  • Row 1: 55 cells
  • Row 2: 66 cells
  • Row 3: 66 cells
  • Row 4: 55 cells
  • Row 5: 55 cells
  • Row 6: 55 cells
  • Row 7: 55 cells

Total number of cells:

=5+6+6+5+5+5+5=37\begin{aligned} &= 5 + 6 + 6 + 5 + 5 + 5 + 5 \\ &= 37 \end{aligned}
  • A valid Hidato puzzle of 3737 cells must only contain numbers from 11 to 3737.
  • The given numbers are: 1,2,4,6,12,13,17,21,23,26,30,31,34,36,391, 2, 4, 6, 12, 13, 17, 21, 23, 26, 30, 31, 34, 36, 39.
  • The number 3939 is greater than the total number of cells (3737).
Answer

(ii) Puzzle 2 cannot be solved as a standard Hidato puzzle.

(iii) Solve Puzzle 3.

Step 1 · Count Cells and Compare Given Values

Count the number of cells in each row:

  • Row 1: 11 cell
  • Row 2: 22 cells
  • Row 3: 55 cells
  • Row 4: 77 cells
  • Row 5: 77 cells
  • Row 6: 77 cells
  • Row 7: 55 cells
  • Row 8: 11 cell

Total number of cells:

=1+2+5+7+7+7+5+1=35\begin{aligned} &= 1 + 2 + 5 + 7 + 7 + 7 + 5 + 1 \\ &= 35 \end{aligned}
  • A valid Hidato puzzle of 3535 cells must only contain numbers from 11 to 3535.
  • The given numbers are: 1,5,7,9,10,15,17,23,25,26,28,29,34,35,39,42,44,49,50,54,561, 5, 7, 9, 10, 15, 17, 23, 25, 26, 28, 29, 34, 35, 39, 42, 44, 49, 50, 54, 56.
  • The numbers 39,42,44,49,50,54,5639, 42, 44, 49, 50, 54, 56 are all greater than the total number of cells (3535).
Answer

(iii) Puzzle 3 cannot be solved as a standard Hidato puzzle.

Common Mistakes
  • Assuming Missing Numbers: Trying to force a path without first verifying that the largest given number does not exceed the total cell count NN.
  • Miscounting Irregular Grids: Multiplying overall width by height instead of summing the individual cells in non-rectangular grids.

More questions in A

Q1

Investigate how traditional calendars in India managed to consistently align the days in the calendar with astronomical events like the Earth going around the Sun or even the positions of the stars in the sky accurately.

Q2

Try solving the following Hidato puzzles.

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