supose that you have three diffrent lenghts of linking cubes as shown below assume that you have as many of these lenghts as you need but you may not take them apart
can you make each lenghts below using only one colour if it is possible show more than one way
a) 25 cubes
B)20 cubes
c)18 cubes
d)29 cubes
E) 30 cubes
f)32 cubes
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how do you not know this
To determine if each length can be made using only one color, let's analyze the given lengths of linking cubes:
a) 25 cubes: This length cannot be made using only one color because it is an odd number, and the linking cubes are likely to be in pairs of two for each color.
b) 20 cubes: This length can be made using only one color. One possible way is to use 20 linking cubes of the same color.
c) 18 cubes: This length cannot be made using only one color because it is not a multiple of 5.
d) 29 cubes: This length cannot be made using only one color because it is a prime number and cannot be divided into equal parts.
e) 30 cubes: This length can be made using only one color. One possible way is to use 30 linking cubes of the same color.
f) 32 cubes: This length can be made using only one color. One possible way is to use 32 linking cubes of the same color.
In summary:
- Lengths a) and c) cannot be made using only one color.
- Lengths b), e), and f) can be made using only one color.
- Length d) cannot be made using only one color.
To solve this problem, we need to determine if it is possible to make each of the given lengths using the linking cubes without taking them apart. Let's analyze each length separately:
a) 25 cubes
To make 25 cubes, you need to represent the number 25 using the available lengths. Let's assume the lengths available are A, B, and C.
Possible solution:
- Using length A (10 cubes) and length B (15 cubes)
- Using length A (10 cubes) and length C (5 cubes)
- Using length B (15 cubes) and length C (10 cubes)
b) 20 cubes
To make 20 cubes, you again need to represent the number 20 using the available lengths (A, B, and C).
Possible solution:
- Using length A (10 cubes) and length B (10 cubes)
- Using length C (20 cubes)
c) 18 cubes
To make 18 cubes, we need to find a way to represent this number using the available lengths (A, B, and C).
Possible solution:
- There is no combination of lengths A, B, and C that can form exactly 18 cubes.
d) 29 cubes
To make 29 cubes, we need to find a way to represent this number using the available lengths (A, B, and C).
Possible solution:
- There is no combination of lengths A, B, and C that can form exactly 29 cubes.
e) 30 cubes
To make 30 cubes, we need to find a combination of lengths that will equal this number.
Possible solution:
- Using length A (10 cubes), length B (10 cubes), and length C (10 cubes)
f) 32 cubes
To make 32 cubes, we need to find a combination of lengths that will equal this number.
Possible solution:
- Using length A (10 cubes), length B (10 cubes), and length C (12 cubes)
In summary:
a) 25 cubes: Multiple solutions possible
b) 20 cubes: Multiple solutions possible
c) 18 cubes: Not possible
d) 29 cubes: Not possible
e) 30 cubes: One solution possible
f) 32 cubes: One solution possible