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2017-04-24 Basic

         

Four open containers of equal volume are connected as shown.

If the capacity of the pipes is greater than the flowrate from the tap, which container will fill first?

AB+CDEF \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 EF? \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,IA, B, C, D, E, F, G, H, I all lie on a circle, as shown above, find A+B+C+D+E+F+G+H+I\angle A+\angle B+\angle C+\angle D+\angle E+\angle F+\angle G+\angle H+\angle I in degrees.

123412431324134214231432412341324213423143124321 \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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