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If the digit 9 is ignored when summing the digits, the effect is to "cast out" one more 9 to give the result 12. More generally, when casting out nines by summing digits, any set of digits which add up to 9, or a multiple of 9, can be ignored. In the number 3264, for example, the digits 3 and 6 sum to 9.
Note: The reason why this works is that if we have: a+b=c and b is a multiple of any given number n, then a and c will necessarily produce the same remainder when divided by n. In other words, in 2 + 7 = 9, 7 is divisible by 7. So 2 and 9 must have the same remainder when divided by 7. The remainder is 2.
A complex question, trick question, multiple question, fallacy of presupposition, or plurium interrogationum (Latin, 'of many questions') is a question that has a complex presupposition. The presupposition is a proposition that is presumed to be acceptable to the respondent when the question is asked. The respondent becomes committed to this ...
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The number 19 is not a harshad number in base 10, because the sum of the digits 1 and 9 is 10, and 19 is not divisible by 10. In base 10, every natural number expressible in the form 9R n a n, where the number R n consists of n copies of the single digit 1, n > 0, and a n is a positive integer less than 10 n and multiple of n, is a harshad ...
A regular towel can do the trick, or you can invest in an easy-to-clean blanket designed for sex, like the Liberator Throw. You’ll also want to prepare yourself by drinking some water ahead of time.
For example, to say that 14 × 15 was 201 would be unreasonable. Since 15 is a multiple of 5, the product should be as well. Likewise, 14 is a multiple of 2, so the product should be even. Furthermore, any number which is a multiple of both 5 and 2 is necessarily a multiple of 10, and in the decimal system would end with a 0. The correct answer ...
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