\[\sum_{i=1}^9i^3=2025=\left(\sum_{i=1}^9i\right)^2\]

\[\sum_{i=1}^9i^3=2025=\left(\sum_{i=1}^9i\right)^2\]

\[1^3+2^3+3^3+4^3+5^3+6^3+7^3+8^3+9^3=2025\]

\[\sum_{i=1}^9i^3=2025=\left(\sum_{i=1}^9i\right)^2\]

\[1^3+2^3+3^3+4^3+5^3+6^3+7^3+8^3+9^3=2025\]

\[(1+2+3+4+5+6+7+8+9)^2=2025\]

\[\sum_{i=1}^9i^3=2025=\left(\sum_{i=1}^9i\right)^2\]

\[\sum_{i=1}^9i^3=2025=\left(\sum_{i=1}^9i\right)^2\]

\[\sum_{i=1}^9i\times i^2=45^2\]

\[\sum_{i=1}^9i\times i^2=45^2\]

\[\sum_{i=1}^9i\times i^2=45^2\]

\[\sum_{i=1}^9i\times i^2=45^2\]

mscroggs.co.uk/squares

\[\sum_{i=1}^9i^3=\left(\sum_{i=1}^9i\right)^2\]

\[\sum_{i=1}^9i^3=\left(\sum_{i=1}^9i\right)^2\]

\[n\]

\[n\]

IMPOSSIBLE

IMPOSSIBLE

IMPOSSIBLE

IMPOSSIBLE

IMPOSSIBLE

IMPOSSIBLE

2332 solutions

216285 solutions

doi.org/10.5281/zenodo.17058519

[[17, 7, 1], [22, 13, 2], [22, 15, 2], [9, 26, 3], [9, 29, 3], [18, 29, 3], [18, 13, 4], [29, 8, 4], [33, 8, 4], [33, 20, 4], [24, 0, 5], [24, 5, 5], [24, 10, 5], [24, 15, 5], [33, 24, 5], [9, 32, 6], [12, 26, 6], [15, 32, 6], [18, 7, 6], [18, 17, 6], [18, 23, 6], [9, 38, 7], [16, 38, 7], [17, 0, 7], [23, 38, 7], [38, 24, 7], [38, 31, 7], [38, 38, 7], [9, 0, 8], [29, 0, 8], [29, 12, 8], [30, 29, 8], [30, 37, 8], [37, 0, 8], [37, 8, 8], [37, 16, 8], [0, 0, 9], [0, 9, 9], [0, 18, 9], [0, 27, 9], [0, 36, 9], [9, 8, 9], [9, 17, 9], [21, 29, 9], [24, 20, 9]]

[[29, 27, 1], [35, 5, 2], [35, 7, 2], [0, 0, 3], [3, 0, 3], [12, 25, 3], [20, 23, 4], [31, 5, 4], [37, 24, 4], [41, 24, 4], [7, 25, 5], [15, 23, 5], [22, 0, 5], [27, 0, 5], [32, 0, 5], [0, 3, 6], [0, 30, 6], [6, 30, 6], [24, 21, 6], [31, 9, 6], [31, 15, 6], [0, 9, 7], [0, 16, 7], [0, 23, 7], [15, 0, 7], [15, 7, 7], [24, 14, 7], [30, 21, 7], [7, 9, 8], [7, 17, 8], [12, 28, 8], [29, 28, 8], [37, 0, 8], [37, 8, 8], [37, 16, 8], [37, 28, 8], [0, 36, 9], [6, 0, 9], [9, 36, 9], [15, 14, 9], [18, 36, 9], [20, 27, 9], [22, 5, 9], [27, 36, 9], [36, 36, 9]]

[[14, 30, 1], [32, 31, 2], [34, 31, 2], [0, 18, 3], [3, 18, 3], [6, 18, 3], [0, 37, 4], [0, 41, 4], [23, 5, 4], [32, 33, 4], [17, 0, 5], [22, 0, 5], [31, 9, 5], [31, 14, 5], [31, 19, 5], [9, 24, 6], [14, 31, 6], [17, 5, 6], [17, 11, 6], [20, 31, 6], [26, 31, 6], [0, 30, 7], [7, 30, 7], [15, 24, 7], [17, 17, 7], [22, 24, 7], [24, 17, 7], [29, 24, 7], [4, 37, 8], [9, 0, 8], [9, 8, 8], [9, 16, 8], [12, 37, 8], [20, 37, 8], [23, 9, 8], [28, 37, 8], [0, 0, 9], [0, 9, 9], [0, 21, 9], [27, 0, 9], [36, 0, 9], [36, 9, 9], [36, 18, 9], [36, 27, 9], [36, 36, 9]]

[[30, 38, 1], [21, 24, 2], [23, 24, 2], [0, 42, 3], [3, 42, 3], [6, 42, 3], [8, 0, 4], [8, 4, 4], [15, 20, 4], [21, 26, 4], [9, 15, 5], [14, 15, 5], [31, 24, 5], [31, 29, 5], [31, 34, 5], [9, 20, 6], [9, 26, 6], [9, 32, 6], [15, 24, 6], [25, 24, 6], [30, 39, 6], [0, 8, 7], [7, 8, 7], [9, 38, 7], [14, 8, 7], [16, 38, 7], [21, 8, 7], [23, 38, 7], [0, 0, 8], [12, 0, 8], [15, 30, 8], [20, 0, 8], [23, 30, 8], [28, 0, 8], [28, 8, 8], [28, 16, 8], [0, 15, 9], [0, 24, 9], [0, 33, 9], [19, 15, 9], [36, 0, 9], [36, 9, 9], [36, 18, 9], [36, 27, 9], [36, 36, 9]]

[[6, 31, 1], [14, 14, 2], [27, 15, 2], [16, 14, 3], [33, 9, 3], [33, 12, 3], [7, 24, 4], [7, 28, 4], [19, 24, 4], [19, 28, 4], [6, 32, 5], [11, 32, 5], [14, 9, 5], [23, 29, 5], [23, 34, 5], [0, 31, 6], [16, 39, 6], [22, 39, 6], [23, 17, 6], [23, 23, 6], [27, 9, 6], [0, 9, 7], [0, 24, 7], [7, 9, 7], [16, 17, 7], [16, 32, 7], [29, 15, 7], [29, 22, 7], [0, 16, 8], [0, 37, 8], [8, 16, 8], [8, 37, 8], [11, 24, 8], [19, 9, 8], [28, 29, 8], [28, 37, 8], [0, 0, 9], [9, 0, 9], [18, 0, 9], [27, 0, 9], [36, 0, 9], [36, 9, 9], [36, 18, 9], [36, 27, 9], [36, 36, 9]]

[[23, 17, 1], [29, 17, 2], [32, 7, 2], [9, 38, 3], [19, 34, 3], [31, 9, 3], [0, 41, 4], [4, 41, 4], [8, 41, 4], [15, 34, 4], [22, 27, 5], [22, 32, 5], [24, 17, 5], [24, 22, 5], [34, 7, 5], [8, 0, 6], [8, 6, 6], [8, 12, 6], [9, 32, 6], [39, 0, 6], [39, 6, 6], [8, 18, 7], [8, 25, 7], [12, 38, 7], [15, 27, 7], [31, 12, 7], [32, 0, 7], [38, 12, 7], [0, 0, 8], [0, 8, 8], [0, 16, 8], [0, 24, 8], [19, 37, 8], [23, 9, 8], [29, 19, 8], [37, 19, 8], [0, 32, 9], [14, 0, 9], [14, 9, 9], [15, 18, 9], [23, 0, 9], [27, 27, 9], [27, 36, 9], [36, 27, 9], [36, 36, 9]]

[[30, 21, 1], [21, 22, 2], [23, 22, 2], [18, 0, 3], [18, 3, 3], [24, 6, 3], [0, 28, 4], [0, 32, 4], [12, 23, 4], [21, 24, 4], [7, 23, 5], [16, 22, 5], [30, 16, 5], [35, 16, 5], [40, 16, 5], [0, 0, 6], [6, 0, 6], [12, 0, 6], [21, 0, 6], [24, 16, 6], [25, 22, 6], [0, 14, 7], [0, 21, 7], [24, 9, 7], [31, 9, 7], [31, 21, 7], [38, 9, 7], [38, 21, 7], [0, 6, 8], [4, 28, 8], [8, 6, 8], [16, 6, 8], [16, 14, 8], [21, 28, 8], [29, 28, 8], [37, 28, 8], [0, 36, 9], [7, 14, 9], [9, 36, 9], [12, 27, 9], [18, 36, 9], [27, 0, 9], [27, 36, 9], [36, 0, 9], [36, 36, 9]]

[[17, 35, 1], [41, 39, 2], [43, 39, 2], [17, 20, 3], [42, 17, 3], [42, 20, 3], [23, 35, 4], [41, 0, 4], [41, 4, 4], [41, 41, 4], [15, 15, 5], [17, 30, 5], [18, 35, 5], [18, 40, 5], [22, 30, 5], [9, 8, 6], [9, 14, 6], [23, 39, 6], [29, 39, 6], [35, 39, 6], [36, 17, 6], [15, 8, 7], [17, 23, 7], [22, 8, 7], [24, 23, 7], [29, 8, 7], [31, 23, 7], [38, 23, 7], [9, 0, 8], [9, 20, 8], [9, 28, 8], [17, 0, 8], [20, 15, 8], [25, 0, 8], [28, 15, 8], [33, 0, 8], [0, 0, 9], [0, 9, 9], [0, 18, 9], [0, 27, 9], [0, 36, 9], [9, 36, 9], [27, 30, 9], [36, 8, 9], [36, 30, 9]]

[[23, 17, 1], [23, 32, 2], [25, 32, 2], [8, 9, 3], [11, 9, 3], [24, 29, 3], [0, 25, 4], [4, 25, 4], [23, 34, 4], [27, 5, 4], [27, 0, 5], [30, 24, 5], [32, 0, 5], [35, 24, 5], [40, 24, 5], [8, 12, 6], [17, 32, 6], [24, 17, 6], [24, 23, 6], [31, 5, 6], [31, 11, 6], [17, 18, 7], [17, 25, 7], [17, 38, 7], [24, 38, 7], [30, 17, 7], [31, 38, 7], [38, 38, 7], [0, 9, 8], [0, 17, 8], [0, 29, 8], [0, 37, 8], [23, 9, 8], [37, 0, 8], [37, 8, 8], [37, 16, 8], [0, 0, 9], [8, 18, 9], [8, 27, 9], [8, 36, 9], [9, 0, 9], [14, 9, 9], [18, 0, 9], [27, 29, 9], [36, 29, 9]]

[[25, 32, 1], [6, 36, 2], [26, 23, 2], [0, 36, 3], [3, 36, 3], [26, 30, 3], [0, 32, 4], [4, 32, 4], [14, 5, 4], [25, 33, 4], [8, 0, 5], [13, 0, 5], [20, 32, 5], [26, 25, 5], [31, 25, 5], [0, 39, 6], [8, 5, 6], [8, 11, 6], [8, 17, 6], [8, 32, 6], [14, 32, 6], [6, 38, 7], [13, 38, 7], [14, 9, 7], [14, 16, 7], [21, 9, 7], [21, 16, 7], [29, 30, 7], [0, 0, 8], [0, 8, 8], [0, 16, 8], [0, 24, 8], [20, 37, 8], [28, 9, 8], [28, 17, 8], [28, 37, 8], [8, 23, 9], [17, 23, 9], [18, 0, 9], [27, 0, 9], [36, 0, 9], [36, 9, 9], [36, 18, 9], [36, 27, 9], [36, 36, 9]]

[[29, 21, 1], [30, 33, 2], [30, 35, 2], [26, 6, 3], [26, 9, 3], [26, 12, 3], [0, 37, 4], [0, 41, 4], [5, 6, 4], [32, 33, 4], [0, 0, 5], [0, 5, 5], [17, 15, 5], [17, 20, 5], [17, 25, 5], [5, 0, 6], [11, 0, 6], [17, 0, 6], [23, 0, 6], [30, 21, 6], [30, 27, 6], [9, 30, 7], [16, 30, 7], [22, 15, 7], [23, 30, 7], [29, 0, 7], [29, 7, 7], [29, 14, 7], [4, 37, 8], [9, 6, 8], [9, 14, 8], [9, 22, 8], [12, 37, 8], [20, 37, 8], [22, 22, 8], [28, 37, 8], [0, 10, 9], [0, 19, 9], [0, 28, 9], [17, 6, 9], [36, 0, 9], [36, 9, 9], [36, 18, 9], [36, 27, 9], [36, 36, 9]]

[[38, 22, 1], [5, 35, 2], [7, 35, 2], [24, 28, 3], [42, 9, 3], [42, 12, 3], [5, 37, 4], [5, 41, 4], [25, 37, 4], [25, 41, 4], [0, 35, 5], [0, 40, 5], [24, 23, 5], [29, 23, 5], [34, 23, 5], [9, 31, 6], [15, 31, 6], [21, 31, 6], [30, 9, 6], [36, 9, 6], [39, 22, 6], [9, 17, 7], [9, 24, 7], [16, 9, 7], [16, 16, 7], [23, 9, 7], [23, 16, 7], [38, 15, 7], [0, 9, 8], [8, 9, 8], [9, 37, 8], [16, 23, 8], [17, 37, 8], [29, 37, 8], [30, 15, 8], [37, 37, 8], [0, 0, 9], [0, 17, 9], [0, 26, 9], [9, 0, 9], [18, 0, 9], [27, 0, 9], [27, 28, 9], [36, 0, 9], [36, 28, 9]]

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