# Problems of the Week

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# 2018-11-19 Basic

Suppose I have unlimited pennies ($0.01), nickels ($0.05), dimes ($0.10), and quarters ($0.25).

I can produce $0.36 using • 4 coins: 1 quarter, 2 nickels, and 1 penny, • 5 coins: 3 dimes, 1 nickel, and 1 penny, or • 6 coins: 2 dimes, 3 nickels, and 1 penny. Can I also produce$0.36 using exactly 7 coins?

When traffic merges from two lanes to one, will cars be moving faster in the wide or narrow part?

Assume that there is a steady flow of bumper-to-bumper traffic approaching the merge point.

I just got a $10 \times 10$-piece jigsaw puzzle. All of the pieces only fit together one way. Each piece connects to at least two other pieces.

My assembly plan: I'm going to take pieces from the box one by one at random, and fit them together if possible. I'll keep going until all of the pieces taken out fit together in one connected clump.

If I've already taken out two pieces that don't directly connect, what is the maximum number of additional pieces that I might need to draw in order to connect them?

Ram pours some concentrated sugar solution in a thistle funnel, and covers the mouth with parchment paper. He places the thistle funnel upside-down in a beaker containing distilled water, and marks the initial height of the liquid in the funnel.

After 3 hours, what happens to the height of the liquid in the funnel compared to its initial height?

Note: Parchment paper is selectively permeable, meaning that water can pass through, but sugar cannot.

In both of the quadrilaterals (a rectangle and a parallelogram) below, four inner segments extended from the four vertices form a rectangle in the center. At the same time, two congruent triangles are generated on opposite sides.

Must this only occur in rectangles and parallelograms?

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