In Magic Diamond use numbers 1-12. Each row must equal the same sum.
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Start with 1 and 2, and subtract (1+2) from the sum 26:
26 - (1+2) = 23.
Now, since the largest number used will be 12 and we've just used 1 and 2, the remaining edge number must be 11:
23 - 12 = 11
So the first edge set is {1,2,11,12},
the next set is {1,3,10,12}, and
the next is {1,4,9,12}
. . . .
. . . .
Thus we get
{1,2,11,12}
{1,3,10,12}
{1,4, 9,12}
{1,4,10,11}
{1,5,8,12}
{1,5,9,11}
{1,6,7,12}
{1,6,8,11}
{1,6,9,10}
{1,7,8,10}
{2,3,9,12}
. . .
. . .
{5,6,7,8}
Thanks Vinny. But its Diamond with 4 circles each side. one circle common between two sides and the number should not e repeated to use. If i am not mistaken.
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To solve this Magic Diamond puzzle using numbers 1-12, we need to find a pattern where each row equals the same sum. Let's start by placing the numbers in a diamond shape:
1
2 12
11 3
10 4
9 5
8 6
7
Now, we need to find a sum for each row. Let's calculate the sum for each row:
Row 1: 1
Row 2: 2 + 12 = 14
Row 3: 11 + 3 = 14
Row 4: 10 + 4 = 14
Row 5: 9 + 5 = 14
Row 6: 8 + 6 = 14
Row 7: 7
From our calculations, we can see that Row 1 equals 1 and Row 7 equals 7. Now we need to find the sum for Rows 2 to 6, which should all equal the same number.
To find that number, we can add up the values of Row 2 to Row 6, and then divide by the number of rows. Let's do the calculations:
(14 + 14 + 14 + 14 + 14) ÷ 5 = 70 ÷ 5 = 14
So, the sum for Rows 2 to 6 is 14.
The completed Magic Diamond with equal sum for each row is as follows:
1
2 12
11 3
10 4
9 5
8 6
7
The sum for each row is:
Row 1: 1
Row 2: 2 + 12 = 14
Row 3: 11 + 3 = 14
Row 4: 10 + 4 = 14
Row 5: 9 + 5 = 14
Row 6: 8 + 6 = 14
Row 7: 7
The Magic Diamond puzzle involves arranging the numbers 1 to 12 in a diamond shape, where each row must have the same sum of numbers. To solve this puzzle and find the arrangement, you can follow these steps:
1. Start by placing the number 1 at the top of the diamond, as shown in the diagram you provided.
2. Next, look at the rows below the top row. You can see that there are two rows with empty spots. To fill these spots, you need to find numbers that, when added to the numbers above them, will equal the sum of the rows.
3. In this case, for the second row (with 3 empty spots), the sum of the top row is 1. So, you need to find three numbers that add up to 1. The only numbers that work are -4, 0, and 5. So, place these numbers in the empty spots, making sure they don't repeat.
4. Now, look at the third row (with 2 empty spots). The sum of the second row is 1+(-4)+0+5 = 2. So, you need to find two numbers that add up to 2. The only numbers that work are -3 and 5. Place these numbers accordingly.
5. Finally, look at the bottom row (with 1 empty spot). The sum of the third row is 1+(-4)+0+5+(-3)+5 = 4. So, you need to find one number that adds up to 4. The only number that works is -1. Place this number in the empty spot.
By following these steps, you should be able to fill in all the empty spots in the Magic Diamond puzzle and have each row with the same sum.