1996 Puzzle - Solution

The Puzzle:

Use the numerals 1, 9, 9 and 6 exactly in that order to make the following numbers: 28, 32, 35, 38, 72, 73, 76, 77, 100 and 1000

You can use the mathematical symbols +, −, ×, /, √, ^ (exponent symbol) and brackets.

Example: 1 × 9 + 9 × 6 = 63

Our Solution:

1 + 9 + √(9) × 6 = 28
(1/√(9)) × 96 = 32
−19 + (9x6) = 35
19/(√(9)/6) = 38
(1 + √(9))×√(9) × 6 = 72
19 + (9 × 6) = 73
1 + (9 × 9) − 6 = 76
−19 + 96 = 77
1 + √(9) + 96 = 100
(1 + 9)^(9 − 6) = 1000

Robert Veith has worked out all of these:

1 + 9(-√(9) + 6) = 28
19 + √(9) + 6 = 28
1^9 + √(√(9))^6 = 28
1 + √(9)(√(9) + 6) = 28
1 + 9(−√(9) + 6) = 28
1 + 9(9 − 6) = 28
1 + √(9)^(-√(9) + 6) = 28
1 + √(9)^(9 − 6) = 28
1 + √(√(√(√(√(√(9))))))^96 = 28
−1 + √(9)^√(9) + 6 = 32
−1 + 9*√(9) + 6 = 32
−1 + (√(9) + √(9))(6) = 35
−1 + (9 − √(9))(6) = 35
−1 + 9 + √(√(9))^6 = 35
(−1 + 9)(√(9) + 6) = 72
1(9 + √(9))(6) = 72
(1*9 + √(9))(6) = 72
1 + (9 + √(9))(6) = 73
(1 + 9)^√(√(9) + 6) = 1000
√(√(1 + 99))^6 = 1000
(1 + 9)^(−√(9) + 6) = 1000
√(√(√(√(√(1 + 9)^96 = 1000

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