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
28 = 1+9+√(9)×6 32 = (1/√(9))×96 35 = -19+(9x6) 38 = 19/(√(9)/6) 72 = (1+√(9))×√(9)×6 73 = 19+(9×6) 76 = 1+(9×9)-6 77 = -19+96 100 = 1+√(9)+96 1000 = (1+9)^(9-6)
Calculate the number of ordered triples (A1, A2, A3) such that:
A1 ∪ A2 ∪ A3 = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A1 ∩ A2 ∩ A3 = ∅
Write your answer as 2a3b5c7d where a, b, c, d are non-negative integers.
The digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 can be arranged into an addition sum to add up to almost any total, except that nobody has yet found a way to add up to 1984. However 9 digits can equal 1984 by an addition sum. Which digit is omitted?
