Live Challenges 3

[This post originally appeared on the Brilliant blog on 10/5/2012.]

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

Monday: Calvin wants to go from Chicago to Australia for a holiday. He goes online and finds that there are 5 flights from Chicago to Hong Kong, 6 flights from Hong Kong to Singapore, 7 flights from Singapore to Australia, 8 flights from Chicago to Singapore and 4 flights from Hong Kong to Australia. How many different ways can Calvin fly from Chicago to Australia?

Note: The flights are all one-way in the direction specified. In particular, there are no available flights from Singapore to Hong Kong.

Tuesday: Compute the last 3 digits of 171172 171^{172}.

Clarification: If you think that the last 3 digits are 012 012, you may type in either 012 012 or 12 12.

Thursday: The binary operation ⊗ \otimes satisfies a⊗b=ab−4a−4b+20 a \otimes b = ab - 4a - 4b + 20. Determine the value of

1⊗2⊗…⊗20. \sqrt{1} \otimes \sqrt{2} \otimes \ldots \otimes \sqrt{20}.

Note: The order of operations is performed from left to right.

Friday: An integer lattice point is a point with coordinates (n,m) (n, m) , where n n and m m are integers. As N N ranges from 1 to 951, what is the maximum number of integer lattice points in the interior of a triangle with vertices (0,0) (0,0), (N,953−N) (N, 953-N), and (N+1,953−N−1) (N+1, 953-N-1)?

Note: The point (0,0) (0,0) is not in the interior of any of the triangles described above.

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.

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\sin \theta sin⁡θ \sin \theta
\boxed{123} 123 \boxed{123}

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