Mathcounts National Sprint Round Problems And Solutions Hot! May 2026

Cracking the MATHCOUNTS National Sprint Round is the ultimate test for any middle school "mathlete." While Chapter and State rounds test your fundamentals, the National Sprint Round is where speed meets extreme depth.

Recursive Counting: Building a solution based on smaller versions of the same problem. 2. Geometry with a Twist Mathcounts National Sprint Round Problems And Solutions

We can compute:
For each (S), (r = (-2S) \mod 9 = (-2S + 18m) \mod 9). Better: ( -2S \equiv 7S \pmod9) because -2 ≡ 7 mod 9. So (C \equiv 7S \pmod9). Cracking the MATHCOUNTS National Sprint Round is the

• (2 \times 3=6), (2\times5=10), (2\times7=14), (2\times11=22), (2\times13=26), (2\times17=34), (2\times19=38), (2\times23=46), (2\times29=58), (2\times31=62), (2\times37=74), (2\times41=82), (2\times43=86), (2\times47=94) → 14 numbers.
• (3\times5=15, 3\times7=21, 3\times11=33, 3\times13=39, 3\times17=51, 3\times19=57, 3\times23=69, 3\times29=87, 3\times31=93) → 9 numbers.
• (5\times7=35, 5\times11=55, 5\times13=65, 5\times17=85, 5\times19=95) → 5 numbers.
• (7\times11=77, 7\times13=91) → 2 numbers.
• (11\times13=143>100) stop.

Online Resources:

Step-by-Step Solution

1. Solution:
   Total 4-digit numbers: 9000 (from 1000 to 9999).
   Count those with all digits distinct:
   First digit: 1-9 (9 choices). Second: 0-9 except first (9 choices). Third: 8 choices. Fourth: 7 choices.
   Product: 998*7 = 4536.
   So with at least one repeated digit: 9000 - 4536 = 4464. Online Resources: Step-by-Step Solution