TheoremThere exists only one (strictly) positive integer that is exactly twice the sum of its digits. Let $n$ be equal to twice the sum of its digits. Suppose $n$ has $1$ digit. Then $n$ equals the sum of its digits. Thus $n$ does not have only $1$ digit.
Then $n > 99$. But the highest number that can be formed by the sum of $3$ digits is $9 + 9 + 9 = 27$. Similarly for if $n$ has more than $3$ digits.
Let the $2$ digits of $n$ be $x$ and $y$. Thus: \(\ds n\)\(=\)\(\ds 10 x + y\)\(\ds \)\(=\)\(\ds 2 \left({x + y}\right)\)\(\ds \leadsto \ \ \)\(\ds 8 x\)\(=\)\(\ds y\)Since $x$ and $y$ are both single digits, it follows that $x = 1$ and $y = 8$. Hence the result. $\blacksquare$ SourcesRiddle #12: What Number Is Twice The Sum Of Its Digits? By Emery Wood SHARE By Emery Wood Check the answer below: – – – – Answer: The correct number is 18.
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Which number is twice?Two times as many.
What does it mean by sum of twice a number?"SUM" indicates an "ADD" and is always used with the word "AND" to indicate what values are being added. "TWICE" means double, or multiply by 2. Let the number be x. The number is doubled and then 4 is added. Twice a number is 2x.
Which number is the sum of its digits?What is digit sum? We can obtain the sum of digits by adding the digits of a number by ignoring the place values. So, for example, if we have the number 567 , we can calculate the digit sum as 5 + 6 + 7 , which will give us 18 .
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