olymmath

HMMT 2004 U34

  • Guts
  • Answer

Find the number of 20 -tuples of integers x1,…,x10,y1,…,y10x_{1}, \ldots, x_{10}, y_{1}, \ldots, y_{10} with the following properties:

  • 1≤xi≤101 \leq x_{i} \leq 10 and 1≤yi≤101 \leq y_{i} \leq 10 for each ii;
  • xi≤xi+1x_{i} \leq x_{i+1} for i=1,…,9i=1, \ldots, 9;
  • if xi=xi+1x_{i}=x_{i+1}, then yi≤yi+1y_{i} \leq y_{i+1}.

Dataset text NuminaMath olympiads. Quoted with source.

Show the answer

\binom{109}{10}

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.

Add a solution

Similar problems

These problems have the most words in common with this statement.

Locator hmmt/2004/u34 · Tag MXK2G34K1G · Edit this page on GitHub · Keys: j next, k previous