Daily math problems for May 10, 2026 — Combinatorics, Compound Interest, Logarithms

Each preference group must occupy its own seat type. Inside each group, passengers are distinguishable, so they can be permuted freely:

- The 20 window-seekers in the 20 window seats: $20!$ ways - The 30 aisle-seekers in the 30 aisle seats: $30!$ ways - The 50 don't-care passengers in the 50 middle seats: $50!$ ways

The groups are independent, so multiply: $20!\cdot 30!\cdot 50!$.

Each year the value is multiplied by $0.85$. After 4 years: $(0.85{)}^4\approx 0.522$.

Note: *not* $1-4\cdot 0.15=0.40$. Compounding cuts the loss; you don't lose $60\mathrm{\%}$, you lose $\approx 48\mathrm{\%}$.

Energy ratio: ${\displaystyle \frac{{10}^{1.5\cdot 8}}{{10}^{1.5\cdot 6}}}={10}^{1.5\cdot 2}={10}^3=1000$.

A 2-step jump on a base-10 log scale (with the 1.5× exponent factor) corresponds to a ${10}^3=1000\times$ jump in actual energy.