Solution to the Build Your Own Sudoku puzzle
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Solution to the Build Your Own Sudoku puzzle
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May 16, 2026
Build Your Own Sudoku is one of the interesting puzzles of the MIT Mystery Hunt 2014 competition. The plot of the game that year was based on Lewis Carroll's "Alice's Adventures in Wonderland" and "Through the Looking-Glass and what Alice found there." The puzzle featured a blank Sudoku grid with four sets of clues. The first three sets were needed to fill in the puzzle's initial numbers: they corresponded to the sectors, rows and columns of the grid respectively. The last set corresponded to the grid's numbers and was needed to get the answer to the puzzle after solving the Sudoku. The puzzle was part of the Lobby 7 section of the game and was created by Robbie Buckingham.
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Sectors
NorthwestNo square with a given number in the Northwest Sector touches another square with a given number in the same sector along an edge. (In general we say a square touches another if it is the same square or it shares an edge or corner.)<br>NorthThe sum of the given numbers in the North Sector is 13.<br>NortheastThere is a continuous path of touching squares with given numbers from the upper-right corner of the sudoku grid to the lower-left corner of the sudoku grid.<br>WestThe sum of the given numbers in the West Sector is 27, while their product is 1512.<br>CenterRotational symmetry: if there is a given number in any square of the sudoku grid, there is also a (possibly different) given number in the square 180° opposite.<br>EastThe product of the given numbers in the East Sector is 288.<br>SouthwestSquare I1 matches its antipodal square (A9) in the unsolved grid.<br>SouthThe sum of the given numbers in the South Sector is 16.<br>SoutheastThe given numbers in the Southeast Sector are exactly those in the East Sector.
Rows
AThe third square of Row A (A3) matches its antipodal square (I7) in the unsolved grid.<br>BThe given numbers in Row B are exactly those in Column 6.<br>CThe leftmost given number in Row C divides all the other given numbers in its sector.<br>DThe product of the given numbers in D8 and D9 is 16.<br>ENone of the squares with given numbers in Row E are directly above any of the four squares with given numbers in the row below, or directly below any of the squares with given numbers in the row above.<br>FThe sum of the given numbers in Row F, which is the same as the sum of the given numbers in Row D, is 20.<br>GRow G, and every other row, has at least three given numbers.<br>HThe product of the given numbers in H3 and H4 is 72.<br>IThe sum of any given numbers in I1, I2, I3, and I4 is 6 more than the sum of any given numbers in H1 and H2, but 3 less than the sum of any given numbers in Column 5.
Columns
1The product of any given numbers in D1, E1, F1, and G1 is 63.<br>2The product of the given numbers in Column 2 is 18 more than the product of any given numbers in the Northeast Sector.<br>3The sum of the given numbers in Column 3 is 17.<br>4The three squares with given numbers in Column 4 are touching.<br>5There is only one given number in Column 5.<br>6There is only one square with a given number touching G6.<br>7None of the four squares with given numbers in Column 7 touch each other.<br>8There are the same number of squares with given numbers touching A8 as there are touching B8.<br>9The product of the given numbers in Column 9 is 180.
Numbers
1 = A1 × B7 + C5 − ?<br>2 = B2 × C5 + D2 − ?<br>3 = C3 × D7 + E3 − ?<br>4 = D4 × E9 + F3 − ?<br>5 = E5 × F4 + G7 − ?<br>6 = F6 × G1 + H5 − ?<br>7 = G7 × H9 + I5 − ?<br>8 = H8 × I3 + A3 − ?<br>9 = I9 × A9 + B1 − ?
Solution
We will mark the squares of the Sudoku grid that must contain a number using the symbol '*' and the squares that must remain empty using the symbol 'x'.
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According to the clues for the Column 5 and the Center Sector the Column 5 will contain only one number in the middle, in the square E5.
123456789<br>Aх<br>Bx<br>Cx<br>Dx<br>E*<br>Fx<br>Gx<br>Hx<br>Ix<br>Let's consider the clue for the Column 8, taking into account the definition of touching of squares given in the clue for the Northwest Sector. In the Northeast Sector the squares A7, A8, A9, B7, B8, B9 touching both the squares A8 and B8; and the squares C7, C8, C9 touching only the square B8. Thus, numbers could be in any of the squares A7, A8, A9, B7, B8, B9, but cannot be in the squares C7, C8, C9. Symmetrically (clue for the Center Sector), the squares G1, G2, G3 will be empty.
123456789<br>Aх<br>BxCxxxx<br>Dx<br>E*<br>Fx<br>Gxxxx<br>Hx<br>Ix
According to the clue for the Northeast Sector the squares A9, C6, G4, I1 will be filled.
123456789<br>Aх*<br>BxCx*xxx<br>Dx<br>E*<br>Fx<br>Gxxx*x<br>Hx<br>I*x<br>According to the clue for the Row H the squares H3 and H4 will be filled. Symmetrically, the squares B6 and B7 will be filled.
123456789<br>Aх*<br>Bx**Cx*xxx<br>Dx<br>E*<br>Fx<br>Gxxx*x<br>H**x<br>I*x
According to the clue for the Column 4 the squares A4, B4, C4, D4, E4 will be empty. Symmetrically, the squares E6, F6, G6, H6, I6 will be...