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Each of the digits $1,2,3,4,5,6$ is used exactly once in forming the $3$-digit integers $X$ and $Y$. How many possible values of $X+Y$ are there if $|X-Y|=111?$

 

Two boys and three girls are going to sit around a table with $5$ different chairs. If the two boys want to sit together, in how many possible ways can they be seated?

 

What fraction of all the $10$-digit numbers with distinct digits have the property that the sum of every pair of neighboring digits is odd?

 Apr 23, 2021
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1. There are 8 possible values of X + Y.

 

2. There are 60 possible seatings.

 

3. The fraction is 1/5000.

 May 22, 2021

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