Page 24 - NUMINO Challenge_D2

Problem solving Key Points

1 A castle wall has 100 gates numbered 1 to 100. The numbers on the
When 100 guards check the gates by walking opened gates have
around the castle wall every morning in the an odd number of
following ways, how many gates are opened? factors. Think about
the numbers that
The first guard opens all the gates. have an odd number
The second guard closes the gates with even of factors.
numbers.
The third guard closes the opened gates and
opens the closed gates numbered with
multiples of 3.
The fourth guard closes the opened gates and
opens the closed gates numbered with
multiples of 4.
The rest of the guards close the opened gates
and open the closed gates accordingly.

2 Find the greatest 2-digit number that has three The number that has
factors. an odd number of
factors is a square
number.

21Number and Operations