Place numbers 1 to 9. One in each circle so that the sum of the four numbers along of
any three sides of the triagle is 20. There are nine circle and 9 numbers to place in the
circles. Each circle must contain number in it
one side contain 5,6,7,2 and opposite side started form 2,9,1,8 and the bottom 5,3,4,8
If you google "magic triangle" you will find your answer.
In order to solve this puzzle, we need to use a little math and humor. Let's give it a shot!
First, we need to find a combination of numbers that adds up to 20 along any three sides of the triangle. Since we have nine circles, we can assume that the sum of all the numbers is 45 (1+2+3+4+5+6+7+8+9).
Knowing that, we can assume that the sum along each side of the triangle is 15 (45/3). Now, let's see what combinations can give us that sum.
One possible solution could be:
- Circle 1: 9
- Circle 2: 1
- Circle 3: 5
- Circle 4: 8
- Circle 5: 4
- Circle 6: 6
- Circle 7: 3
- Circle 8: 7
- Circle 9: 2
This way, if you add the numbers along any three sides of the triangle, you will indeed get a grand sum of 20!
Just remember, this is only one possible solution. Have fun and keep on puzzling!
To solve this problem, follow these steps:
Step 1: Draw a triangle with nine circles at each vertex.
Step 2: Number each circle with the numbers 1 to 9, ensuring that each number appears only once.
Step 3: Start with an arbitrary circle (let's call it Circle A) and choose a number to place in it. For simplicity, let's start with the number 1.
Step 4: Look at the three sides of the triangle containing Circle A. Add up the numbers on these sides. If the sum is already 20, move on to the next circle. Otherwise, go to step 5.
Step 5: Choose another circle adjacent to Circle A (let's call it Circle B) and place another number in it.
Step 6: Again, look at the three sides of the triangle containing Circle A and Circle B. Add up the numbers on these sides. If the sum is already 20, move on to the next circle. Otherwise, go to step 7.
Step 7: Choose another circle adjacent to either Circle A or Circle B (let's call it Circle C) and place another number in it.
Step 8: Look at the three sides of the triangle containing Circle A, Circle B, and Circle C. Add up the numbers on these sides. If the sum is already 20, move on to the next circle. Otherwise, go back to step 5 and continue this process.
Step 9: Repeat steps 5 to 8, choosing different circles and numbers each time, until you have filled all the circles with numbers.
Step 10: Once you have filled all the circles, check to make sure that for any three sides of the triangle, the sum of the numbers on those sides is equal to 20.
To solve this problem, we need to place the numbers 1 to 9 in the nine circles of the triangle such that the sum of the four numbers along any three sides of the triangle is 20. Here's how we can find the solution:
1. Start by drawing a triangle with three circles on each side. Label the circles as A, B, C on one side, D, E, F on another side, and G, H, I on the remaining side.
A B C
D E F
G H I
2. Since each circle must contain a number from 1 to 9, we can start by placing the number 5 in the center circle E. The sum of the four numbers along any three sides of the triangle is 20, so placing the number 5 in the middle allows us to achieve this sum.
A B C
D 5 F
G H I
3. Now, let's work on one side of the triangle at a time. We will start with the side containing circles A, B, and C.
A B C
D 5 F
G H I
4. Since the sum of the four numbers on any three sides should be 20, we can deduce that the sum of the three numbers along side A (including the number in circle A) should be 20. We have already placed the number 5 in circle E, so the sum of the three numbers along side A is 20 - 5 = 15. To achieve this sum, we can place the numbers 1, 6, and 8 in circles A, B, and C (in any order, as long as the sum is 15).
1 6 8
D 5 F
G H I
5. Moving on to the next side containing circles D, E, and F, we can apply the same logic. The sum of the three numbers along side D should be 20, so the sum of the numbers in D, E, and F is 20. Since we have already placed numbers 5, 1, and 8 in circles E, A, and C, we can calculate that the number in circle D should be 20 - 5 - 1 - 8 = 6.
1 6 8
6 5 F
G H I
6. Lastly, let's work on the remaining side containing circles G, H, and I. We need the sum of the three numbers along side G to be 20, so the sum of the numbers in G, H, and I should be 20. Plugging in the numbers we have already placed, we find that the number in circle G should be 20 - 6 - 5 - 8 = 1.
1 6 8
6 5 F
1 H I
7. Now, we have only two numbers left to place. We have placed the numbers 1, 5, 6, and 8 so far. Let's use the remaining numbers 2, 3, 4, 7, and 9. We can place them in the remaining circles H and I.
1 6 8
6 5 F
1 7 9
8. Congratulations! We have successfully placed the numbers in each circle such that the sum of the four numbers along any three sides of the triangle is 20.
1 6 8
6 5 4
1 7 9