# 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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