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[Mathimagics]

And now for something completely different ...

Consider the following grid:

SUD_Composition_0001.jpg (44.19 KiB) Viewed 1105 times

Taking each row and column of the grid as a 9-digit number, can you write a composition for each value?

A composition is an arithmetic expression that uses each of the digits 1 to 9 once, and only once, and one or more standard arithmetic operators: (+, -, *, /, ^). Division (including negative exponentiation) must always be exact, ie: result in an integer. You may join digits together (but not all 9), and parenthesize as necessary.

Examples:

• 123475896 = 9 * 34 * 718 * 562

• 123475968 = 3456 * (189^2 + 7)

[Mathimagics]

Solutions (Row compositions):

Hidden Text: Show

• Row 1: 391576248 = ((6 * 7)^5 - (12^4 - 9) * 8) * 3

• Row 2: 458192673 = ((4^8 - 5) * 92 - 1) * 76 - 3

• Row 3: 762384951 = ((7^6 + 3) * (2 - 8)^4) * 5 - (9 * 1)

• Row 4: 124658739 = (61^4 + 5 * 27 * 38) * 9

• Row 5: 986713425 = ((5^6 + 81)^2 - 79) * 4 - 3

• Row 6: 573249816 = ((4^7 + 6 * 91)^2 + 8) * (5 - 3)

• Row 7: 645837192 = ((41 * 83 - 7)^2 - 9) * 56

• Row 8: 219465387 = (28^4 + 93) * 7 * 51 - 6

• Row 9: 837921564 = ((2 + 9)^7 - 5 - 618) * 43

Solutions (Col compositions)

Hidden Text: Show

• Col 1: 347195628 = 468 * (12^5 + 79^3)

• Col 2: 956287413 = (2^(3 * 8) - 4 * 61) * 57 + 9

• Col 3: 182463597 = ((26 - 9)^4 - 5 * 18) * 3^7

• Col 4: 513672849 = 263 * (4 + 5^9) - (78 * 1)

• Col 5: 798514362 = (47 - 2 + (6 * 59)^3) * 18

• Col 6: 624839751 = ((6 + 5 * 81)^3 + 4 * 27) * 9

• Col 7: 269748135 = (4^7 + (6 - 1) * 8 )^2 + 359

• Col 8: 475321986 = ((6^7 - 5) * 2 - 1) * 849 - 3

• Col 9: 831956274 = 426 * (5^9 + 7 - 183)