Using the 9 digits, 1, 2, 3, 4, 5, 6,7, 8 and 9 you can arrange four different digits to form a four-digit number that is NOT divisible by 7. The digits 1238 cannot be arranged to create a four-digit number that is divisible by 7. The digits 1389 also cannot be arranged to form a four-digit number that is divisible by 7. Find one additional set (not 1238 or 1389) of four different digits that is not divisible by 7. Provide the digits to form the smallest four digit value.
Please explain.
Double Thanks to the person who helps me with this one.
easy. if you add or subtract 7, or a multiple of 7 to those number, they will not be divisible by 7.
1238-n*7
or 1238+n7. let n=1 ++++ 1245 not divisible by 7
1**** Enter 2 missing digits at index 4 from end
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25
To find an additional set of four different digits that is not divisible by 7, we can use a similar approach. Let's consider the following steps:
1. From the given nine digits (1, 2, 3, 4, 5, 6, 7, 8, 9), we need to choose four different digits to form a four-digit number.
2. First, we need to identify the digits that are divisible by 7. From the given digits, we can see that 7 is divisible by 7. Therefore, we cannot use the digit 7 in the four-digit number.
3. Now, let's try to arrange the remaining digits (1, 2, 3, 4, 5, 6, 8, 9) in different orders to form a four-digit number.
4. Starting with the smallest possible four-digit number, we can arrange the digits in ascending order. Thus, we can start by arranging the digits in increasing order (for example, 1234).
5. We need to check if the number formed by these four digits is divisible by 7. We can use a divisibility rule for 7, which states that if a number is divisible by 7 when its last digit is removed and twice the removed digit is subtracted from the remaining number, then the original number is divisible by 7. Let's apply this rule.
- For 1234: Removing the last digit results in 123. Twice the removed digit (4) is 8. Subtracting 8 from 123 gives us 115, which is not divisible by 7.
- We can continue this process for other combinations of the remaining digits (1356, 1456, 1468, etc.) until we find a combination that results in a four-digit number that is not divisible by 7.
After following this process, we find that the next set of four different digits that is not divisible by 7 (other than 1238 or 1389) is 1456. The smallest four-digit number that can be formed using these digits is 1456.