-- List the digits that are used to write the number.
-- Add up the list.
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Oh, dude, you want me to find 4-digit numbers where the digits add up to 2? That's like finding a needle in a haystack! But hey, I'm up for the challenge. The only number that fits the bill is 1001. So, there you go, one lonely 4-digit number with a digit sum of 2.
Let's go through the process: Add 1 to 456: 456 1 = 457 456+1=457 (does not contain the digit 4) Add 2 to 456: 456 2 = 458 456+2=458 (does not contain the digit 4) Add 3 to 456: 456 3 = 459 456+3=459 (does not contain the digit 4) Add 4 to 456: 456 4 = 460 456+4=460 (contains the digit 4) Here, adding 4 gives us 460, which includes the digit 4. Therefore, the smallest number you can add to 456 to get a sum that uses the digit 4 is 4 4 Read More...tinyurl .com/sx3dkfpw
1002 = 10000 which is the smallest possible 5 digit number. So we have to go 1 smaller which is 992 = 9801
100
No. To be divisible by 6 the number must be divisible by both 2 and 3. To be divisible by 2, the last digit of the number must be even (ie one of {0, 2, 4, 6, 8}). The last digit of 35 is 5 which is not even and so 35 is not divisible by 2. To be divisible by 3, sum the digits of the number and if this sum is divisible by 3 then so is the original number. As the test can be applied to the sum, repeatedly summing the digits of the sums until a single digit remains, then the original number is divisible by 3 only if this single digit is one of {3, 6, 9}. For 35 3 + 5 = 8 which is not divisible by 3 (nor is is one of {3, 6, 9}, thus 35 is not divisible by 3. As 35 is not divisible by both 2 and 3 (in fact it is divisible by neither 2 nor 3) it is not divisible by 6.