I have the following problem

A Three digit natural number's cross sum amounts to $14.$ When you read the number from right to left and subtract $22$, you obtain double the original number. Also the middle digit is equal to the sum of the outer two digits. Find the number

I am not sure what a cross sum is, and have been unable to find resources on it. We have been learning about matrices and know what a cross product is... but not a cross sum.

  • $\begingroup$ Sum of digits is the only plausible interpretation. $\endgroup$ – barak manos Feb 14 '15 at 11:18
  • $\begingroup$ am i right in thinking this should be solved with matrices? as per the second hint the ordering of the numbers is important. So that fits with matrices... $\endgroup$ – Arden Feb 14 '15 at 11:23
  • $\begingroup$ Well, you can solve it either with a $3\times3$ matrix, or with plain math over $3$ equations in $3$ variables... $\endgroup$ – barak manos Feb 14 '15 at 11:31

You have the following equations (under the restriction of $0\leq{a,b,c}\leq9$):

  • $a+b+c=14$
  • $100c+10b+a-22=2(100a+10b+c)$
  • $b=a+c$

This is a system of $3$ equations in $3$ variables, which should be easy to solve:

  • $a=2$
  • $b=7$
  • $c=5$

Hence the number is $275$.

  • $\begingroup$ @Arden: I moved the solution steps out of the answer, because inferring from your question, I'm pretty sure that you can handle the equation-system yourself. $\endgroup$ – barak manos Feb 14 '15 at 11:30

If your question is just asking what a cross sum is, then a cross sum is just the sum of all digits of the given number.

  • 1
    $\begingroup$ Could you provide a reference, please? $\endgroup$ – Adrian Keister May 8 '18 at 17:14
  • $\begingroup$ What sort of reference would you like? Here's an example: The cross sum of 10 is 1+0 = 1 ; the cross sum of 275 = 2 + 7 + 5 = 14 (this happens to be the answer to the question above) . $\endgroup$ – Nikil Kumar Sep 21 '18 at 16:58
  • $\begingroup$ I'm talking about a reference to your definition. What you're referring to as the "cross sum" I'm more used to thinking of as the "digit sum". So if you could point to a mathematical dictionary or reference work of some kind defining "cross sum" the way you have it here, that'd be what I'm asking. $\endgroup$ – Adrian Keister Sep 21 '18 at 17:17
  • $\begingroup$ Well, I came across this word a few times in math class and also in a 'numberphile' video a long time ago, in case you're familiar with that. I haven't found any other reference. $\endgroup$ – Nikil Kumar Sep 21 '18 at 17:20

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.