# Four vagabonds - math puzzle

A very rich lady goes with a bag of coins (not more than 400) to the city. In the city she meets four vagabonds. She gives the first vagabond 4 coins and a quarter of the number of coins which is left in the bag. She applies the same procedure to the second, third and fourth vagabond (so division by 4 worked always). With how many coins did she leave home?

# Thousand monkeys - math puzzle

A very big building in which thousand monkeys are living is lighted by
thousand lamps. Every lamp is connected to a unique on/off switch, which are numbered from 1 to 1000. At some moment, all lamps are switched off. But because it is becoming darker, the monkeys would like to switch on the lights. They will do this in the following way.

Monkey 1 presses all switches that are a multiple of 1.

Monkey 2 presses all switches that are a multiple of 2.

Monkey 3 presses all switches that are a multiple of 3.

Monkey 4 presses all switches that are a multiple of 4.

Etc., etc.

How many lamps are switched on after monkey 1000 pressed his switches? And which lamps are switched on?

Monkey 1 presses all switches that are a multiple of 1.

Monkey 2 presses all switches that are a multiple of 2.

Monkey 3 presses all switches that are a multiple of 3.

Monkey 4 presses all switches that are a multiple of 4.

Etc., etc.

How many lamps are switched on after monkey 1000 pressed his switches? And which lamps are switched on?

# Horse friends - math puzzle

Three horses are standing in a triangular field, which is exactly 100
yards on each side. One horse stands at each corner; and simultaneously
all three set off running. Each horse runs after the horse in the
adjacent corner on his left, thus following a curved course, which
terminates in the middle of the field, all three horses arriving there
together.
The horses obviously ran at the same speed, but just how far did they
run?