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# Solve this. $\square \text{ }+\,\text{ }\square \text{ }+\,\text{ }\square \text{ }=30$. Fill the boxes using (1,3,5,7,9,11,13,15). You can also repeat the numbers.

Last updated date: 21st Jun 2024
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Hint: Sum of 2 odd numbers is always an even, so when we add another number to it, it will become an odd number. Our plan should be that we need to make a number even such that (even)+(odd)+(odd)=30 .

Let us first learn a lesson
1.Adding two even numbers always gives us an even number. Adding two or more even numbers will also give us an even number.
2.Adding two odd numbers will always give us an even number. (eg: $11+7=18$ ) and adding an odd number of even numbers of times will also give an even number (just basic).
3.Now adding three odd numbers will always give us an odd number $(e g: 15+13+3=31)$
4.Adding an odd and an even number will give us an odd number $(\mathrm{eg}: 7+2=9)$
Mathematically we can't solve this question.
Logically it can be solved as,
$(11+3)+9+7=30$ (by adding)
$11+13+3!=30$ (by multiplying or factorial)
$(7-1)+11+13=30$ (by subtracting)
$13.3+5.7+11=30$ (by decimal using numbers 13,3,5,7,11)
The conclusion is that the question needs to be more specific. If we play around with these numbers, there will be an infinite number of ways to solve this.

Note: Most people think that only members of the set need to be used, which gives incorrect answers like ${-}+15+15=30$ or 11 $+13+3 !=30$. These are proper subsets of the set-in question and would not constitute using the set to fill in the blanks. Secondly, the question does not restrict the user from using any other operands, decimals or members of other sets. This would be the case if it stated "using only".