Daily Math · 2026-05-10

Question 1

An airline cabin has 100 seats: 20 windows, 30 aisles, 50 middles. Of the 100 passengers, 20 strictly want a window, 30 strictly want an aisle, and 50 don't mind. How many seat assignments make every preference happy? (Assume passengers are distinguishable; only count the assignments.)

Accepted Answer

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: $20! \cdot 30! \cdot 50!$.

Answer

$20! \cdot 30! \cdot 50!$

Answer

$100!$

Answer

$\binom{100}{20}$

Answer

$50!$

Question 2

A car loses $15\%$ of its value each year. After $4$ years, what fraction of its original value remains?

Accepted Answer

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 $60\%$, you lose $\approx 48\%$.

Answer

$0.40$

Answer

$0.52$

Answer

$0.60$

Answer

$0.85$

Question 3

The Richter scale is logarithmic: a magnitude $M$ earthquake releases roughly $10^{1.5 M}$ units of energy. How many times more energy does a magnitude 8 earthquake release than a magnitude 6 earthquake?

Accepted Answer

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

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

Answer

$2$

Answer

$100$

Answer

$1{,}000$

Answer

$\approx 31{,}600$

Problems & worked solutions

Problem 1 — Combinatorics

Problem 2 — Compound Interest

Problem 3 — Logarithms