Consider the following numbers 3, 6, 9, 12, . . . , 75. Show
that if...
Consider the following numbers 3, 6, 9, 12, . . . , 75. Show
that if we pick 15 arbitrary numbers from them, then we will find
two that have sum equal to 81. I understand that there are 12
distinct sets containing pairs that sum to 81 plus a singleton
subset {3}. but wouldn't this mean that there are 2 remaining
"empty holes" that need to be filled? Not sure how to apply the
pigeonhole principle here.
How many diffrent two-digit numbers can you use the
digits 4,3,7,1,2,6, and 9 without repetition? For...
How many diffrent two-digit numbers can you use the
digits 4,3,7,1,2,6, and 9 without repetition? For example, 77 is
not allowed
The number of diffrent two-digit number is
ou might think that if you looked at the first digit in randomly
selected numbers that...
ou might think that if you looked at the first digit in randomly
selected numbers that the distribution would be uniform. Actually,
it is not! Simon Newcomb and later Frank Benford both discovered
that the digits occur according to the following distribution:
(digit, probability)
(1,0.301),(2,0.176),(3,0.125),(4,0.097),(5,0.079),(6,0.067),(7,0.058),(8,0.051),(9,0.046)(1,0.301),(2,0.176),(3,0.125),(4,0.097),(5,0.079),(6,0.067),(7,0.058),(8,0.051),(9,0.046)
The IRS currently uses Benford's Law to detect fraudulent tax data.
Suppose you work for the IRS and are investigating an individual
suspected of embezzling. The first digit of 166 checks to a
supposed company...
How many valid 3 digit numbers can you make using the
digits 0, 1, 2 and...
How many valid 3 digit numbers can you make using the
digits 0, 1, 2 and 3 without
repeating the digits? How about with repeating?
Pigeonhole Principle:
What is the minimum number of students that must be assigned to
a classroom...
Pigeonhole Principle:
What is the minimum number of students that must be assigned to
a classroom with 14 tables to guarantee that some table will have
at least 3 students?
Suppose a set of 8 numbers are selected from the set {1, 2, 3,
..., 13, 14}. Show that two of the selected numbers must sum to 15.
(Hint: think about how many subsets of 2 elements you can form such
that the sum of the values of the two...
You might think that if you looked at the first digit in
randomly selected numbers that...
You might think that if you looked at the first digit in
randomly selected numbers that the distribution would be uniform.
Actually, it is not! Simon Newcomb and later Frank Benford both
discovered that the digits occur according to the following
distribution: (digit, probability)
(1,0.301),(2,0.176),(3,0.125),(4,0.097),(5,0.079),(6,0.067),(7,0.058),(8,0.051),(9,0.046)(1,0.301),(2,0.176),(3,0.125),(4,0.097),(5,0.079),(6,0.067),(7,0.058),(8,0.051),(9,0.046)
The IRS currently uses Benford's Law to detect fraudulent
tax data. Suppose you work for the IRS and are investigating an
individual suspected of embezzling. The first digit of 145 checks
to a supposed company...