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A daily ritual for math-brained humans. One fresh quiz drops every morning at 6am — three problems, sized for a coffee break.

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Daily · 2026-05-10

Three problems · Combinatorics, Compound Interest, Logarithms

One bite-sized math problem set for the day. Read the statement, think it through, then expand the solution to check your reasoning.

#1 · Combinatorics·Medium
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.)
  1. A.20!⋅30!⋅50!20! \cdot 30! \cdot 50!
  2. B.100!100!
  3. C.(10020)\binom{100}{20}
  4. D.50!50!
Solution
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!20! ways
- The 30 aisle-seekers in the 30 aisle seats: 30!30! ways
- The 50 don't-care passengers in the 50 middle seats: 50!50! ways

The groups are independent, so multiply: 20!⋅30!⋅50!20! \cdot 30! \cdot 50!.
The everyday version of an assignment problem. With more nuanced preferences (Carol wants window OR middle but not aisle) this becomes a proper bipartite matching / Hungarian-algorithm question. Airlines really do solve this kind of problem — though with much messier preference data.
#2 · Compound Interest·Easy
A car loses 15\% of its value each year. After 4 years, what fraction of its original value remains?
  1. A.0.400.40
  2. B.0.520.52
  3. C.0.600.60
  4. D.0.850.85
Solution
Each year the value is multiplied by 0.850.85. After 4 years: (0.85)4≈0.522(0.85)^4 \approx 0.522.

Note: *not* 1−4⋅0.15=0.401 - 4 \cdot 0.15 = 0.40. Compounding cuts the loss; you don't lose 60\%, you lose ~48\%.
Compounding works in both directions. Compounded gains grow faster than linear; compounded losses shrink faster than linear. Same math as the credit-card problem from May 7 — just with rr replaced by −r-r.
#3 · Logarithms·Medium
The Richter scale is logarithmic: a magnitude MM earthquake releases roughly 101.5M10^{1.5 M} units of energy. How many times more energy does a magnitude 8 earthquake release than a magnitude 6 earthquake?
  1. A.22
  2. B.100100
  3. C.1,0001{,}000
  4. D.≈31,600\approx 31{,}600
Solution
Energy ratio: 101.5⋅8101.5⋅6=101.5⋅2=103=1000\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 103=1000×10^3 = 1000\times jump in actual energy.
Why news reports about earthquakes feel so misleading. A 'magnitude 8' isn't 33\% bigger than a 'magnitude 6' — it's a thousand times more energy. Logarithmic scales compress huge ranges into small numbers, which is great for plotting and terrible for intuition.

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