?
Give your answer in denary.
Note:
denotes the rising factorial
denotes the falling factorial
For more information about rising and falling factorials, check out the Wikipedia article .
Hint: Perform the calculations in the brackets then remove the brackets.
Bonus: In the discussion, convert the answer to hexadecimal.
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2 ( 5 ) = 2 ( 2 + 1 ) ( 2 + 2 ) ( 2 + 3 ) ( 2 + 4 ) = 2 ( 3 ) ( 4 ) ( 5 ) ( 6 ) = 7 2 0
4 ( 3 ) = 4 ( 4 + 1 ) ( 4 + 2 ) = 4 ( 5 ) ( 6 ) = 1 2 0
7 2 0 + 1 2 0 = 8 4 0
4 6 ( 3 ) = 4 6 ( 4 6 + 1 ) ( 4 6 + 2 ) = 4 6 ( 4 7 ) ( 4 8 ) = 1 0 3 7 7 6
8 4 0 × 1 0 3 7 7 6 = 8 7 1 7 1 8 4 0
( 4 ) 5 = 4 ( 4 − 1 ) ( 4 − 2 ) ( 4 − 3 ) ( 4 − 4 ) = 4 ( 3 ) ( 2 ) ( 1 ) ( 0 ) = 0
A = 1 0
F = 1 5
8 7 1 7 1 8 4 0 F − 1 0
8 × 1 6 8 + 7 × 1 6 7 + 1 × 1 6 6 + 7 × 1 6 5 + 1 × 1 6 4 + 8 × 1 6 3 + 4 × 1 6 2 + 0 × 1 6 1 = 8 × 4 2 9 4 9 6 7 2 9 6 + 7 × 2 6 8 4 3 5 4 5 6 + 1 × 1 6 7 7 7 2 1 6 + 7 × 1 0 4 8 5 7 6 + 1 × 6 5 5 3 6 + 8 × 4 0 9 6 + 4 × 2 5 6 + 0 × 1 6 = 3 6 2 6 3 0 0 3 1 5 1 + 1 5 = 3 6 2 6 3 0 0 3 1 6 6
3 6 2 6 3 0 0 3 1 6 6 − 1 0 = 3 6 2 6 3 0 0 3 1 5 6
Answer: → 3 6 2 6 3 0 0 3 1 5 6
For the Bonus:
3 6 2 6 3 0 0 3 1 5 6
Convert to hexadecimal:
8 7 1 7 1 8 4 1 4
Bonus Answer: → 8 7 1 7 1 8 4 1 4