Carl thought of 5 numbers and told Danny all the sums that could be made by adding the numbers in pairs. The list of sums is given below. What are the five numbers? 6,7,8,8,9,9,10,10,11,12?
2,4,5,6,6 comes close. It has one 9 and two 11's
See what you can do with it.
To find the five numbers that Carl thought of, we need to analyze the given list of sums. Let's break down the list and find patterns:
6 = the sum of the two lowest numbers
7 = (6 + 1) or (7 + 0), the sum of the second lowest number with either the lowest number or itself
8 = the sum of 2 different numbers greater than 6
8 = (9 - 1) or (8 + 0), the sum of the second highest number with either the lowest number or itself
9 = (10 - 1) or (9 + 0), the sum of the highest number with either the lowest number or itself
9 = (8 + 1) or (9 + 0), the sum of the second highest number with either the second lowest number or itself
10 = (9 + 1), the sum of the second highest number with the lowest number
10 = (10 + 0), the sum of the highest number with itself
11 = (10 + 1), the sum of the highest number with the lowest number
12 = the sum of the two highest numbers
From this analysis, we can conclude that the five numbers that Carl thought of are: 6, 7, 8, 9, and 12.
To find the five numbers, let's start by analyzing the given sums.
First, let's identify all the unique sums:
6, 7, 8, 9, 10, 11, 12
From this list, we can infer that the highest number that can be obtained by adding two numbers together is 12. Therefore, the largest number among the five must be 12.
Now, let's examine the list and look for any repeated sums:
8, 9, 10
There are three repeated sums: 8, 9, and 10. This indicates that the smallest number among the five is 8.
Next, let's consider the remaining unique sums and look for any patterns:
6, 7, 11, 12
Notice that the difference between each of these sums is 1. This suggests that the remaining numbers are consecutive.
Therefore, the five numbers that Carl thought of are: 8, 9, 10, 11, and 12.