# Sunday Afternoon Maths XXX

**Posted on 2014-10-05**

## No change

"Give me change for a dollar, please," said the customer.

"I'm sorry," said the cashier, "but I can't do it with the coins I have. In fact, I can't change a half dollar, quarter, dime or nickel."

"Do you have any coins at all?" asked the customer.

"Oh yes," said the cashier, "I have $1.15 in coins."

Which coins are in the cash register?

(The available coins are 50¢, 25¢, 10¢ 5¢ and 1¢.)

## Dirty work

Source: Futilty Closet

Timothy, Urban, and Vincent are digging identical holes in a field.

When Timothy and Urban work together, they dig 1 hole in 4 days.

When Timothy and Vincent work together, they dig 1 hole in 3 days.

When Urban and Vincent work together, they dig 1 hole in 2 days.

Working alone, how long does it take Timothy to dig one hole?

## Square in a triangle

Source: Maths Jam

A right-angled triangle has short sides of length \(a\) and \(b\). A square is drawn in the triangle so that two sides lie on the sides of the triangle and a corner lies on the hypotenuse.

What is the length of a side of the square?

If you enjoyed these puzzles, check out Advent calendar 2019,

puzzles about polygons, or a random puzzle.

puzzles about polygons, or a random puzzle.