Mathcounts National Sprint Round Problems And Solutions ((better))

Succeeding on the National Sprint Round requires more than just knowing math; it requires optimized execution. Mental Math and Speed Shortcuts

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Here are examples of the type of problems found on the National Sprint Round, demonstrating the logic needed to solve them. Problem 1: Number Theory (Advanced) Succeeding on the National Sprint Round requires more

23S=1323=12two-thirds cap S equals one-third over two-thirds end-fraction equals one-half Now, isolate by multiplying both sides by 32three-halves 7² divides 20!.

⌊20/3⌋+⌊20/9⌋=6+2=8the floor of 20 / 3 end-floor plus the floor of 20 / 9 end-floor equals 6 plus 2 equals 8 So, 3⁸ divides 20!. ⌊20/5⌋=4the floor of 20 / 5 end-floor equals 4 So, 5⁴ divides 20!. For p = 7: ⌊20/7⌋=2the floor of 20 / 7 end-floor equals 2 So, 7² divides 20!.