write a number 1,3,5,7,9,11,13,15,17 in each circle so that the sum of the numbers in each side of the triangle is exactly 30. each number can be used only once.
Answers
The sum of all nine given numbers is 81.
The sum of all three sides of the triangle is 3 x 30 = 90
Three numbers in the corners will be counted twice in the sum of 90,
so the sum of the three numbers in the corners must be 90 - 81 = 9
The only way to get a sum of 9 with three of the given numbers is to take 1, 3 and 5. So those are the three numbers in the corners. It doesn't matter which of these three numbers gets put in each corner.
Consider the side with 1 and 3 at its ends: the sum of the remaining two circles must be 30 - 1 - 3 = 26.
The only way to get 26 with the remaining numbers is to use 17 and 9, or 11 and 15.
Consider the side with 3 and 5 at its ends: the sum of the remaining two circles must be 30 - 3 - 5 = 22.
The only way to get 22 with the remaining numbers is to use 7 and 15, or 9 and 13.
Consider the side with 1 and 5 at its ends: the sum of the remaining two circles must be 30 - 1 - 5 = 24.
The only way to get 24 with the remaining numbers is to use 7 and 17, or 9 and 15.
There are nine numbers and nine circles so each number must be used once.
Looking back at the possible combinations, the only one to use 11 is side 1,3, so one side must be 1,11,15,3.
Likewise the only side to use 13 is 3,5, so a second side must be
3,13,9,5.
This leaves only two numbers unused, making the third side:
1,7,17,5
Of course the order of the middle two numbers in each side doesn't matter, nor does the order in which the three sides are displayed.
Answer:
1-3-5+7-9+11+13+15=30
Step-by-step explanation:
First, just add up all the numbers. (As a shortcut, you can add 1 to 15 and get 16, add 3 to 13 and get 16, etc. to get 4 sets of 16, which is 64. But there are few enough numbers here you can also just add them by hand.)
1+3+5+7+9+11+13+15=64
So we overshot by 34. If we reverse a number, subtracting it instead of adding it, we reduce the total by double the amount. So we want to take enough numbers to add up to 17 and subtract them instead of add them. There are 3 different pairs of numbers that add to 16 (7+9, 5+11, and 3+13) and then add the 1 to any of those to make 17. You could also do it with 3, 5, and 9 to get 17, giving you 4 options. Let’s go with 3, 5, and 9 just because then we can use all the numbers in order and don’t have to start with a negative number. That gives us this solution:
1-3-5+7-9+11+13+15=30
That is a solution that uses all numbers, one time each, in order, using only addition and subtraction and no negative numbers (so don’t start with -1).
First understand
- ODD X ODD = ODD
- EVEN X EVEN = EVEN
- ODD X EVEN = EVEN
- ODD + ODD = EVEN or ODD
- (If odd numbers are added even times result is always even. eg 7+3=10. if odd numbers are added odd times result is always odd. eg 7+3+27= 37)
ODD + EVEN = ODD
So the answer of your question is : yes we can make 30 out from the odd number series by adding it even times.
eg 1+9+7+13=30 :: 3+7+9+11=30 and many more.
Link
- https://brainly.in/question/168135
- https://brainly.in/question/17185666