The answer is zero. Here's why:

1. Let's assume that there is at least one multiple of 3 among the ten numbers.

2. If a number is a multiple of 3, then adding or subtracting any whole number to/from it will result in a number that is either a multiple of 3 or not, depending on the whole number added or subtracted.

3. However, the problem states that the sum and the difference of any two adjacent numbers are not multiples of 3.

4. This means that no number in the sequence can be a multiple of 3, because adding or subtracting it with its adjacent number(s) could potentially result in a multiple of 3, which contradicts the conditions given in the problem.

5. Therefore, none of the ten whole numbers can be multiples of 3.

Question

The answer is zero. Here's why:

1. Let's assume that there is at least one multiple of 3 among the ten numbers.

2. If a number is a multiple of 3, then adding or subtracting any whole number to/from it will result in a number that is either a multiple of 3 or not, depending on the whole number added or subtracted.

3. However, the problem states that the sum and the difference of any two adjacent numbers are not multiples of 3.

4. This means that no number in the sequence can be a multiple of 3, because adding or subtracting it with its adjacent number(s) could potentially result in a multiple of 3, which contradicts the conditions given in the problem.

5. Therefore, none of the ten whole numbers can be multiples of 3.

Knowee AI · Accepted Answer

The answer is zero. Here's why:

1. Let's assume that there is at least one multiple of 3 among the ten numbers.

2. If a number is a multiple of 3, then adding or subtracting any whole number to/from it will result in a number that is either a multiple of 3 or not, depending on the whole number added or subtracted.

3. However, the problem states that the sum and the difference of any two adjacent numbers are not multiples of 3.

4. This means that no number in the sequence can be a multiple of 3, because adding or subtracting it with its adjacent number(s) could potentially result in a multiple of 3, which contradicts the conditions given in the problem.

5. Therefore, none of the ten whole numbers can be multiples of 3.

Ten whole numbers are arranged in a row so that the sum and the difference of any two adjacent numbers are not multiples of 3. How many of these ten whole numbers are multiples of 3?

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