1990 AMC 8 Problem 12
Attempt Problem 12 of the 1990 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1990 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
12.
There are twenty-four -digit whole numbers that use each of the four digits and exactly once. Listed in numerical order from smallest to largest, the number in the th position in the list is
Answer: B
Small hint:
The numbers split into four blocks of by their leading digit
Big hint:
Positions – start with , – start with , – start with ; find the th number starting with
Solution:
Each leading digit accounts for of the numbers. Positions – begin with , positions – begin with , and positions – begin with .
So the th number is the th one beginning with : . The fifth is .
Thus, the correct answer is B .
Problem 12 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
- 1995 AMC 8
- 1996 AMC 8
- 1997 AMC 8
- 1998 AMC 8
- 1999 AMC 8
- 2000 AMC 8
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