Problems - 1999 Winter Open, Division B
PROBLEM 1: Unique Quotients [Piele]
The letters A..J each represent a different single digit from the set [0..9]. Find all solutions to the quotient of two five digit numbers:
ABCDE / FGHIJ = 9
Note: leading zeros are allowed, i.e., F could be 0.
INPUT FORMAT:
A single integer N that specifies which solution of the set to print.
SAMPLE INPUT (file INPUT.TXT);
1
OUTPUT FORMAT:
Print the two integers that represent ABCDE and FGHIJ with a space between them on a line. Print only the Nth solution from the set of solutions ordered numerically smallest ABCDE first.
SAMPLE OUTPUT (file OUTPUT.TXT):
57429 06381
[Problem|Data|Solutions]
PROBLEM 2: Reciprocal Omissions [Eliot W. Collins]
For each n in the integers 1..9 find the smallest m such that 1/m is a repeating decimal whose repeating part contains all the digits 0..9 except n. The repeating part might include some digits more than once.
INPUT FORMAT:
A single line containing N (1 <= N <= 9)
SAMPLE INPUT (file INPUT.TXT):
2
OUTPUT FORMAT:
A single line containing m and the first 25 digits of its decimal expansion after any leading zeros.
SAMPLE OUTPUT (file OUTPUT.TXT):
324 3086419753086419753086419
[Problem|Data|Solutions]
PROBLEM 3: Checks [1991 ACM, Texas A&M University]
Checks contain their value written both numerically and as words. Write a program to read a positive dollar amount less than a trillion, with two decimal places, and display the amount in words.
Here is the output for 64325.28:
SIXTY FOUR THOUSAND THREE HUNDRED TWENTY FIVE AND TWENTY EIGHT/100 DOLLARS
Notice that the word "AND" only appears before the hundredths. Spelling counts! Traditional American counting rules apply. Feel free to ask if you have a very specific question.
INPUT FORMAT:
A single line containing a dollar amount less than a trillion dollars.
SAMPLE INPUT (file INPUT.TXT):
123.45
OUTPUT FORMAT:
A single line with the word representation of the number exactly as patterned here.
SAMPLE OUTPUT (file OUTPUT.TXT):
ONE HUNDRED TWENTY THREE AND FORTY FIVE/100 DOLLARS
[Problem|Data|Solutions]
PROBLEM 4: Long Multiplication [1995 ACM Regional]
Given a pair of numbers, show the complete long multiplication result:
123
95
-----
615
1107
-----
11685
INPUT FORMAT:
Two lines, each with a positive integer. Each integer will have from 1 through 20 digits.
SAMPLE INPUT (file INPUT.TXT):
123
456
OUTPUT FORMAT:
The lines that would be written when doing the multiplication manually. Do not print the dashed lines. Do not print spaces in front of the numbers. The output will contain three lines plus one line for each digit of the second integer.
SAMPLE OUTPUT (file OUTPUT.TXT):
123
456
738
615
492
56088
[Problem|Data|Solutions]