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Logic Level 1

The digits used in the next sentence are all equal. The number of times the digit _______ is used in this sentence is _______ . \begin{array}{|l|} \hline \text{The digits used in the next sentence are all equal.} \\ \text{The number of times the digit } \text{\_\_\_\_\_\_\_} \text{ is used in this sentence is } \text{\_\_\_\_\_\_\_}. \\ \hline \end{array}

If each of the missing numbers in the blanks is a single-digit number, what is the sum of all the missing numbers?

4 5 6 3

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1 solution

Tapas Mazumdar
Sep 12, 2016

Consider statement 1 :

The digits used in the next sentence are all equal. \text{The digits used in the next sentence are all equal.}

So we know that both the blanks must be filled with the same digit (digits from 1 1 to 9 9 inclusive).

Consider statement 2 :

The number of times the digit_____is used in this sentence is_____ . \text{The number of times the digit} \text{\_\_\_\_\_} \text{is used in this sentence is} \text{\_\_\_\_\_}.

Now, whatever the digit we use to fill one of the blanks will be same digit that is to be filled in the other blank (condition from statement 1 ).

Also, the number of times we use the digit will be the equal to the number of blanks we put it in (condition from statement 2 ). Further we can deduce that the digit to be used is equal to the number of blanks it has to be filled in .

\therefore The digit that satisfies the criteria is 2 2 .

And sum of the missing digits: 2 + 2 = 4 2+2=\boxed{4} .

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