Sunday, October 19, 2014

285: Three Angles Revisited

Two days ago, I posted Okay for a Fifth-Grader?

Five Triangles said, "We posed the question slightly differently, our diagram providing an important hint to bring it to a more manageable level for younger problem solvers."


What do you suppose the "important hint" was?


Saturday, October 18, 2014

284: Analyzing Digits


When the integers from 1 to 30 are multiplied, determine how many consecutive digits starting from the ones (1s) position are zeros.
Why does this question not require a calculator?

Would this be a fair question for some standardized test?

source.

Friday, October 17, 2014

283: Ok for a Fifth-Grader?

Three squares of equal but unknown size.


Is this a fair question to ask a fifth-grader?


From a Numberphile video.

Thursday, October 16, 2014

282: Number puzzle


"The sum of two positive integers is 216. The greatest common factor of the two numbers is 24. What are all the possible pairs of numbers?"

What approach seems the easiest here?
I can see using solution methods such as:
  • algebra
  • guess and check
  • organized list
  • visual representation
Which (or which other) method rings true for you?
Which of the two sentences eliminates the most numbers?

Wednesday, October 15, 2014

Tuesday, October 14, 2014

280: Rectangular Nets of Maximum Size - Connected

One possible arrangement.
If you wish, you can consider this problem to be one of wrapping paper around a small gift.

Find the net for the rectangular prism with the largest volume that you can make from a standard piece of paper (8.5" x 11"). Use whatever net arrangement of sides you prefer, but it has to be one connected net. (No loose pieces).

Find the sizes of the six rectangular pieces that form the rectangular prism with the largest volume that can be made from a standard piece of paper (8.5" x 11").

Monday, October 13, 2014

279: Rectangular nets of Maximum Size - Separate Pieces

Using a single sheet of 8.5x11 paper ... cover a rectangular solid. You can cut the paper.

What arrangement of rectangles seems to work best to cover it with no waste?

Which set of rectangles covers the prism with the largest possible volume?


"Find the sizes of the six rectangular pieces that can be made from a standard piece of paper (8.5" x 11") that that will cover the rectangular prism with the largest volume."