Daily Maths Challenges

189 readers

1 users here now

Share your cool maths problems.

Complete a challenge:

Post your solution in comments, if it is exactly the same as OP's solution, let us know.
Have fun.

Post a challenge:

Doesn't have to be original, as long as it is not a duplicate.
Challenges not riddles, if the post is longer than 3 paragraphs, reconsider yourself.
Optionally include solution in comments, let it be clear this is not a homework help forums.
Tag [unsolved] if you don't have a solution yet.
Please include images, if your question includes complex symbols, attach a render of the maths.

Feel free to contribute to a series by DMing the OP, or start your own challenge series.

founded 6 months ago

MODERATORS

[email protected]

Find a+b (lemmy.world)

submitted 6 months ago* (last edited 6 months ago) by [email protected] to c/[email protected]

8 comments fedilink hide all child comments

The image is of a large unit square with five smaller disjoint shaded squares contained entirely within it. The five smaller squares are congruent. Four of them are at each corner of the large square. The fifth is in the center, rotated diagonally, so the center of each of its sides is touched by the vertex from one of the other four squares. You are given that the common length for the five smaller congruent squares is (a-sqrt(2)) / b, where a and b are positive integers. What is the value of a + b?

you are viewing a single comment's thread
view the rest of the comments

[–] [email protected] 3 points 6 months ago* (last edited 6 months ago) (1 children)

All good 👍

spoilerish commentary

This is the short / simple solution I mentioned in my other comment. I think when I originally encountered this problem (well over a year ago) I tackled it by making an equation that added to 1, the side length of the unit square - but picking the diagonal makes everything work out far, far simpler.

Also, not sure if you care, but that link allows full access to everything in your drive.

[–] [email protected] 5 points 6 months ago (1 children)

holdup taking the side length of the unit square actually makes the working out a bit simpler, because the otherside is 1

idk i just saw the diagonal at first

2l+0.5 sqrt(2l^2)=1
l(2+0.5sqrt(2))=1
l=1/(2+0.5sqrt(2))
=(2-0.5sqrt(2))/3.5
=(4-sqrt(2))/7

also, all the public items on the drive is mean to be public, there are unlisted and private items u dont see

[–] [email protected] 3 points 6 months ago

Hey, you're right. I'm not sure what I did originally to make it so complicated, then ¯\_(ツ)_/¯