Here is my dilemma; I have had no formal instructions with proof writing
or discrete mathematics. I am taking a problem solving class where most
of the solutions are based on discrete mathematics structures. Below
are four questions I need assistance in answering.
How do I prove that in a group of n people there are two people with the
same number of acquaintances within the group? (Am thinking this is a
pigeon hole problem)
Prove that given a sequence of twelve integers, a1, a2, âŚ,a12, there
is a subsequence aj, aj+1, âŚ, ak where 12 divides âkn= aa n.
A scrape of paper is found in an old desk that read:
72 turkeys $X67.9Y
The first and last digits of the price were smudged. What are the two
smudged digits?
Ń
Ń
Ń
not necessarily distinct, one can always choose three of these integers
whose sum is divisible by 3.
Mathematics Homework Solutions
#42752
Discrete Structures : Sequences, Subsequences and Remainders
1. How do I prove that in a group of n people there are two people with the same number of acquaintances within the group?
2. Prove that given a sequence of twelve integers, a1, a2,
,a12, there is a subsequence aj, aj+1,
, ak where 12 divides ∑kn= aa n.
3. A scrape of paper is found in an old desk that read: 72 turkeys $X67.9Y
The first and last digits of the price were smudged. What are the two smudged digits?
4. Show that from any five integers, not necessarily distinct, one can always choose three of these integers whose sum is divisible by 3.
Sequences, Subsequences and Remainders and Proofs are investigated. The solution is detailed and well presented.
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