andy has the cards 1,5,7,
belle has the cards 5,4,7
carol has the cards 2,4,6,
andy draws the question card. do you see 2 or more players who cards sum to the same value? he answered yes. next belle draws the question card. Of the five odd numbers how many odd numbers do you see, she says all of them. andy speaks up I know what I have, he says a1,a5,and a7.summarize the salient facts of the problem. Explain the strategy for solving the problem. present a step by step solution of the problem. Clearly state your answer.
Salient facts of the problem:
- Andy has the cards 1, 5, and 7.
- Belle has the cards 5, 4, and 7.
- Carol has the cards 2, 4, and 6.
- Andy drew the question card and confirmed that there are 2 or more players who have cards that sum to the same value.
- Belle drew the question card and stated that she sees all five odd numbers.
- Andy claims to know what cards he has: a1, a5, and a7.
Strategy for solving the problem:
1. Determine the possible pairs of cards that could sum to the same value.
2. Check if any of the pairs have the same sum.
3. Confirm if Belle's statement about odd numbers is accurate.
4. Analyze Andy's claim and compare it to the previously identified pairs.
Step-by-step solution:
1. Possible pairs of cards that can sum to the same value are:
- Andy(a1) and Belle(b5) with a sum of 6.
- Andy(a5) and Carol(c4) with a sum of 9.
- Belle(b5) and Carol(c7) with a sum of 12.
- Belle(b7) and Carol(c4) with a sum of 11.
2. Since Andy confirmed that there are 2 or more players with cards adding up to the same value, we can see that the pairs:
- Andy(a5) and Carol(c4), and
- Belle(b7) and Carol(c4),
have the same sum of 9.
3. Belle stated that she sees all five odd numbers. We know that Andy has a1, a5, and a7. Therefore, Andy's cards (a1, a5, a7) cover the three odd numbers: 1, 5, and 7.
4. Andy's claim matches with Belle's statement about the odd numbers, and the pairs (a5, c4) and (b7, c4) have the same sum of 9.
Answer: Based on the given information, Andy can see that there are two pairs of cards (a5, c4) and (b7, c4) which sum up to 9.