Suppose that you have three different length of linking cubes as shows below assume that you have as many of these length as you need but you may not take them apart. Can you make each length below using only one clout if it is possible, show more than one way.

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To determine if you can make each length using only one clout (linking cube), we need to examine the given lengths and the available cubes. However, without knowing the actual lengths and the sizes of the linking cubes, I cannot provide specific instructions or demonstrate multiple ways to build each length.

Nevertheless, I can guide you through the general approach to solving such problems:

1. Analyze the given lengths: Take note of the specific measurements for each length mentioned in the problem. For instance, let's assume the lengths are 4 units, 7 units, and 10 units.

2. Assess the available linking cubes: Determine the sizes or lengths of the linking cubes provided. Let's suppose you have linking cubes of size 1 unit each.

3. Explore possible combinations: Based on the given lengths and available linking cubes, consider different ways of combining or arranging the cubes to form each length.

a. Start with the simplest length: If the smallest length is provided, such as 4 units, see if you can create this length using only one clout. Experiment with various arrangements of the linking cubes, ensuring that they equal the desired length when connected.

b. Move on to the other lengths: Repeat the process for the remaining lengths (in this case, 7 units and 10 units) to see if you can achieve them using only one clout. Be creative and explore different arrangements.

4. Record your findings: Document the different ways you were able to construct each length using only one clout. If there are multiple solutions, it's important to include them all.

Remember, the specific lengths and sizes of the linking cubes will greatly affect the potential solutions. Based on the information provided, I cannot offer precise solutions, but by following the above steps, you should be able to determine if each length can be built using only one clout, and if so, discover multiple ways to do so.

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