From 51 to 60
3 Write a number 1, 3, 5, 7, 9, 11, 13, 15 or 17 in each
circle so that the sum of the numbers in each circle
on each side of the triangle is exactly 30. Each
number can be used only once.
Answers
Answer:
this is your answer, hope it help
(1,11,15,3), (1,7,17,15), (3,13,9,5)
The total of the nine numbers provided is 81.
The triangle's three sides add up to 3 x 30 = 90.
In the sum of 90, the three numbers in the corners will be counted twice.
so 90 - 81 = 9 must be the result of adding the three digits in the corners.
Take 1, 3, and 5 in order to generate a sum of 9 using three of the above integers. Thus, the three numbers in the corners are as follows. Which of these three numbers is placed in each corner is irrelevant.
The sum of the remaining two circles must be 30 - 1 - 3 = 26 when the side with 1 and 3 at its ends is taken into consideration.
With the remaining numbers, either 17 and 9 or 11 and 15 must be used to arrive to 26.
The sum of the remaining two circles must be 30 - 3 - 5 = 22 when the side with 3 and 5 at its ends is taken into consideration.
With the remaining numbers, only the combinations of 7 and 15 or 9 and 13 will yield the number 22.
The sum of the remaining two circles must be 30 - 1 - 5 = 24 when the side with 1 and 5 at its ends is taken into consideration.
The only remaining digits that add up to 24 are 7 and 17 or 9 and 15.
Each number can only be used once because there are nine circles and nine numbers.
One side must be 1,11,15,3 after looking back at the possible combinations and seeing that the only one to use 11 is side 1,3.
Similarly, the only side of 13 that can be used is 5, hence a second side must be
3,13,9,5.
With only two numbers remaining, the third side becomes:
1,7,17,5
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