June 2026 Problem of the Month

I saw the sign below at my carwash last month and I always take the challenge when someone says, "Do the Math."

However, on this plaque, the "math ain't mathin'" so your challenge is to fix the math.
It reads,
618 cars / day
4,640 cars / week
18,560 cars / month
What numbers need to be changed?

Solution to the Problem:

Here are some solutions:

The simplest way to fix the math is to assume that the 618 car washes per day is correct.
Then the sign should read 4,326 cars per week (not 4,640 cars).
For the number of cars washed per month, it could be one of the following:
28 day month: 17,304 cars per month
30 day month: 18,540 cars per month
31 day month: 19,158 cars per month
If you take the average days per month (365 / 12), then the result is 18,797 cars per month.

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Dr. Kishan writes:
If 8-day weeks and 32-day months are considered then we should have 580 cars/day, 4640 cars/week and 18560 cars/month because 580×8=4640 and 580×32=18560.
If 7-day weeks and 30-day months are considered then we should have 618 cars/day, 4326 cars/week and 18540 cars/month because 6187=4326 and 61830=18540.

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Colin Bowey offers two solutions:
Solution 1: Change the Daily Figure
If the daily figure is increased from 618 cars per day to 662.86 cars per day (or 663 cars per day, rounded), then:

Weekly car washes = 662.86 × 7 = 4,640.02 ≈ 4,640 cars
Monthly car washes = 4,640.02 × 4 = 18,560.08 ≈ 18,560 cars
Therefore, changing the daily figure to approximately 663 cars per day makes the weekly and monthly figures consistent.

Solution 2: Change the Weekly Figure (with a Typographical Error in the Monthly Calculation)
If the daily figure of 618 cars per day is correct, then the weekly figure should be:

618 × 7 = 4,326

The monthly figure of 18,560 cars can be obtained by multiplying 618 by 30.033 days per month:

618 × 30.033 = 18,560.394 ≈ 18,560

It is possible that 30.033 is the result of a typographical error. For example, if someone calculated:
364 ÷ 12 = 30.333
and accidentally typed 30.033 instead of 30.333, then the monthly figure of approximately 18,560 cars would result.
Therefore, if the daily figure is correct and the monthly figure arose from this typographical error, the weekly figure should be corrected from 4,640 to 4,326.

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