Place the numbers 1-10 in the cicrles below. Any number above two others must be their difference.
O
O O
O O O
O O O O
HELP
To solve this problem, we need to follow the given condition: any number above two others must be their difference. Let's break it down step by step.
1. Start by filling in the lowest possible numbers in the circles. Since we have four circles and need to use numbers 1-10, we can start with 1, 2, 3, and 4. Place them as follows:
O
1 2
3 4
O O O
2. Now we need to find the difference between each pair of numbers and place those differences in the circles above them.
- To find the difference between 1 and 2, subtract 1 from 2. The difference is 1. Place it in the first circle above 1 and 2:
O
1 2
1 3 4
O O O
- To find the difference between 2 and 3, subtract 2 from 3. The difference is 1. Place it in the second circle above 2 and 3:
O
1 2
1 3 4
1 1 4
O O O
- To find the difference between 3 and 4, subtract 3 from 4. The difference is 1. Place it in the third circle above 3 and 4:
O
1 2
1 3 4
1 1 4
1 1 1
O O O
3. Continue this pattern of finding the difference between the numbers you have and placing those differences in the next row above:
- Find the difference between 1 and 1 (already placed). The difference is 0. Place it in the fourth circle above the bottom row:
O
1 2
1 3 4
1 1 4
1 1 1
0 1 1
O O O
- Find the difference between 2 and 1 (already placed). The difference is 1. Place it in the final circle above the bottom row:
O
1 2
1 3 4
1 1 4
1 1 1
0 1 1
1 1 1
O O O
4. Finally, fill in the remaining numbers in the circles. By following the difference pattern, you can complete the remaining numbers:
O
1 2
1 3 4
1 1 4
1 1 1
0 1 1
1 1 1
1 1 1
1 1 1
O O O
This arrangement satisfies the given condition, and you have successfully placed the numbers 1-10 in the circles!