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2017-04-24 Basic

         

Four open containers of equal volume are connected as shown. Water slowly comes out of the tap to fill container 1. Due to the connections between containers, water can only flow from one container to the next.

If the capacity of the connecting pipes is greater than the rate of flow of water from the tap, then which container will fill first?

\[ \begin{array} { l l l }
& A & B \\ + & C & D \\ \hline & E & F \\ \end{array} \]

In the above cryptogram, all the letters represent distinct digits.

What is the minimum possible value of the 2-digit integer \( \overline{EF}? \)


Note: In cryptogram problems, 0 is not allowed to be a leading (first) digit, since we would just not write anything in its place.

If points \(A, B, C, D, E, F, G, H, I\) all lie on a circle, as shown above, find \[\angle A+\angle B+\angle C+\angle D+\angle E+\angle F+\angle G+\angle H+\angle I\] in degrees.

\[ \begin{array} { ccccccc }
1234 & 1243 & 1324 & 1342 & 1423 & 1432 \\ \vdots & & & & & \vdots \\ 4123 & 4132 & 4213 & 4231 & 4312 & 4321 \\ \end{array} \]

The 24 distinct 4-digit numbers above have been listed out by arranging 1, 2, 3, and 4 in different orders. What is the sum of these 24 numbers?

\(\)
Hint: You do not need to list out all 24 numbers to find the sum.


From: Derek Niederman's Math Puzzles for the Clever Mind

\(\)
By using 2 straight lines, what is the most number of regions that we can separate the cross into?

Note: Using 1 straight line, it is possible to separate the cross into 3 regions.

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