Live Challenges

[This post originally appeared on the Brilliant blog on 10/21/2012.]

The following challenges will be discussed this coming week. Remember to keep discussion of a challenge to its own blog post.

Monday: There are 100 beads on a necklace. 1 of them is red, the rest are blue. Working in the clockwise direction, we start from the red bead and remove every other bead. Right when the red bead is removed, how many blue beads are there left on the necklace?

Note: The first bead removed is the blue bead that is right next to the red bead in the clockwise direction.

Tuesday: How many ordered pairs of positive integers (a,b) (a, b) are there such that both a2+3b a^2 + 3b and b2+3a b^2 + 3a are perfect squares?

Thursday: P P is a point in rectangle ABCD ABCD. The distance from P P to the 4 vertices of the rectangle are 7,15,24 7, 15, 24 and N N in some order. If N N is an integer, determine the value of N N.

Friday: How many ordered sets of positive integers (x,y,z) (x, y, z) are there such that xyz=3(x+y+z)? xyz= 3(x+y+z)?

Note by Calvin Lin
8 years ago

1 vote

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

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[example link](https://brilliant.org)example link
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print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai−1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 ∑i=13 \sum_{i=1}^3
\sin \theta sin⁡θ \sin \theta
\boxed{123} 123 \boxed{123}

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