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2 cards from this section. Quick, good the night before a test.
List all distinct pairs of integers from the set {1, 2, 3, 4, 5, 6, 7, 8} that sum to 9.
Pair numbers that add up to 9.
If you select the integers 1, 2, 4, 5, what pair (if any) will sum up to 9?
Consider the remaining integers in your set.
How many distinct pairs can sum to 9 from the set {1, 2, 3, 4, 5, 6, 7, 8}?
Count available combinations.
If you choose the integers 1, 4, and 7, will there be at least one pair summing to 9?
Think about missing integers to round out your selected numbers.
If you randomly select 7 integers from the set {1, 2, 3, 4, 5, 6, 7, 8}, can you guarantee at least one sum of 9? Justify your answer using the pigeonhole principle.
Refer back to the pairs you have established.
If a new integer 9 was added to the set, how would that change the original proof regarding sums to 9? Discuss and reason.
Think about how to create new pairs with the existing numbers.
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