Solving an Irregular Clock: No Continuous 576 Minutes

[Jenny Physics]

Homework Statement

A clock runs irregularly but after 24 hours it has neither gained nor lost overall.
Find a way the clock can run irregularly such that there is no continuous 576 minutes during which the clock shows that 576 minutes have passed.

Homework Equations

24 hours = 1440 minutes and $576=\frac{2}{5}1440$.

The Attempt at a Solution

The likely idea is to divide the 24 hours/1440 minutes in a number of intervals and have the clock run faster in odd intervals (say running one hour in 30 minutes), then slower in even intervals (say running one hour in 90 minutes) so that overall it still runs 1440 minutes. I can't get the numbers to work though for 576 minutes.

 

[PeroK]

Homework Statement

A clock runs irregularly but after 24 hours it has neither gained nor lost overall.
Find a way the clock can run irregularly such that there is no continuous 576 minutes during which the clock shows that 576 minutes have passed.

Homework Equations

24 hours = 1440 minutes and $576=\frac{2}{5}1440$.

The Attempt at a Solution

The likely idea is to divide the 24 hours/1440 minutes in a number of intervals and have the clock run faster in odd intervals (say running one hour in 30 minutes), then slower in even intervals (say running one hour in 90 minutes) so that overall it still runs 1440 minutes. I can't get the numbers to work though for 576 minutes.

Think about functions.

 

[Jenny Physics]

Think about functions.

You mean think about a specific function?

 

[PeroK]

You mean think about a specific function?

Not a specific function, but what the graph would look like if you plotted time against time shown on the clock.

 

[Jenny Physics]

Not a specific function, but what the graph would look like if you plotted time against time shown on the clock.

I can imagine all sorts of such functions (sinusoidal, triangular) but not how to go about such that there are no continuous 576 minutes.

 

[PeroK]

I can imagine all sorts of such functions (sinusoidal, triangular) but not how to go about such that there are no continuous 576 minutes.

To keep things simple I would assume the clock can't go backwards. Then the time shown against time is an increasing function.

Have you been studying the intermediate value theorem?

I'm signing off now. Merry Xmas!

 

[WWGD]

Assuming you need to stick to a 24hr period (i.e., no modular aritmetic), notice 1440/576 =25, which is odd, so we could combine increments/changes to cancel each other out...