Math Problem for 2017

January 3, 2017 at 10:11 pm 7 comments

Happy New Year! Welcome to 2017.

Here are some interesting facts about the number 2017:

  • It’s prime. (Okay, so that fact isn’t very interesting. But just you wait…)
  • Insert a 7 between any two digits of 2017, and the result  is still a prime number. That is, 27,017, 20,717, and 20,177 are all prime. (See? Told you it was gonna get better.)
  • The cube root of 2017 is approximately 12.63480759, which uses all ten digits 0‑9, and 2017 is the least positive integer that has this property. (Mind blown yet?)
  • The decimal expansion of 20172017 has 6,666 digits.
  • 2017 = 442 + 92
  • 2017 = 123 + 63 + 43 + 23 + 13 = 103 + 93 + 63 + 43 + 23

If you need some more, check out Matt Parker’s video.

Sorry, no video from me. But in honor of our newly minted prime year, I have created a problem for you to solve.

In the area model below (not to scale), the area of the five blue regions is indicated by the number inside the rectangle. What is the area of the yellow region with the question mark inside?

2017puzzle

Sorry, I don’t give answers. Feel free to have at it in the comments.

Advertisements

Entry filed under: Uncategorized. Tags: , , , , .

Predicting Your Child’s Height, and the Eventual Demise of Our Species 2 Good 2 Be True

7 Comments Add your own

  • 1. xander  |  January 4, 2017 at 4:19 pm

    I’m super-lazy. The five rectangles give five equations in six variables: a*x = 20; a*y=17; b*z=20; c*x=2017; c*z = 17 (the heights of the rectangles are a,b,c from top to bottom, and the widths are x,y,z from left to right). Plug those into Maple to get solutions, then have Maple multiply b*y to find that the mystery area is 2017.

    One could solve this system by hand, but that seems rather tedious, and therefore can’t possibly be the intended method of attack.

    Reply
    • 2. venneblock  |  January 5, 2017 at 7:51 am

      You can’t really “solve” the system by hand, since there are six unknowns but only five equations. I didn’t intend for you to use Maple, but I’m curious… what values did it return for each variable?

      I had an algebraic trick in mind to find the solution, though working with my sons last night, they were far more keen on trying to find values for a, b, c, x, y, and z and then using those values to determine b*y.

      Reply
      • 3. xander  |  January 5, 2017 at 10:36 am

        You can “solve” it by hand in the sense that the system is underdetermined, hence one of the variables is free. Pick your independent variable, then solve everything else in terms of that variable.

        By the way, by hand, I get:

        b*y
        = (20/z)*y (since b*z = 20)
        = (20/17)*c*y (since c*z = 17)
        = (20/17)*(2017/x)*y (since c*x = 2017)
        = (2017/17)*a*y (since a*x = 20)
        = 2017 (since a*y = 17).

        Maple, by the way, does a more complete job of describing all possible solutions, and returns

        {a = 17/y, b = 2017/y, c = 34289/(20*y), x = (20/17)*y, y = y, z = (20/2017)*y}

  • 4. puntomaupunto  |  January 5, 2017 at 9:08 am

    well, 2017 is a solution, but this would mean that the image was taken directly above the model and that what we perceive as “squares” are wiggled surfaces (very wiggled when the value is 2017)

    Reply
  • 5. Carnevale della matematica #105 | backup del Post  |  January 13, 2017 at 10:10 pm

    […] un quizzino di Patrick Vennebush, da cui ho rubato anche le proprietà di cui sopra. Nel disegno qui a destra (non in scala), l’area delle […]

    Reply
  • 6. margit  |  February 8, 2017 at 4:49 pm

    (the heights of the rectangles are a,b,c from top to bottom, and the widths are x,y,z from left to right)

    Since
    ax = bz (=20) ===> b = ax / z
    and
    ay = cz (=17) ===> y = cz / a

    well we are looking for by:

    by = (axcz) / (az) ===> by = xz (and this is 2017)

    Reply
    • 7. margit  |  February 8, 2017 at 5:20 pm

      Sorry
      little mistake in the end

      must be by = xc ( and this is 2017)

      Reply

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

Trackback this post  |  Subscribe to the comments via RSS Feed


About MJ4MF

The Math Jokes 4 Mathy Folks blog is an online extension to the book Math Jokes 4 Mathy Folks. The blog contains jokes submitted by readers, new jokes discovered by the author, details about speaking appearances and workshops, and other random bits of information that might be interesting to the strange folks who like math jokes.

MJ4MF (offline version)

Math Jokes 4 Mathy Folks is available from Amazon, Borders, Barnes & Noble, NCTM, Robert D. Reed Publishers, and other purveyors of exceptional literature.

Past Posts

January 2017
M T W T F S S
« Dec   Feb »
 1
2345678
9101112131415
16171819202122
23242526272829
3031  

Enter your email address to subscribe to the MJ4MF blog and receive new posts via email.

Join 251 other followers

Visitor Locations

free counters

%d bloggers like this: