Lockers and Bulbs

Task 1 (Source: Illustrative Math)

The 20 students in Mr. Wolf's 4th grade class are playing a game in a hallway that is lined with 20 lockers in a row.

• The first student starts with the first locker and goes down the hallway and opens all the lockers.
• The second student starts with the second locker and goes down the hallway and shuts every other locker.
• The third student stops at every third locker and opens the locker if it is closed or closes the locker if it is open.
• The fourth student stops at every fourth locker and opens the locker if it is closed or closes the locker if it is open.

This process continues until all 20 students in the class have passed through the hallway.

1. Which lockers are still open at the end of the game? Explain your reasoning.
2. Which lockers were touched by only two students? Explain your reasoning.
3. Which lockers were touched by only three students? Explain your reasoning.
4. Which lockers were touched the most? 

Factors and Multiples

 source: OCR Maths

 

 

 

 

 

 

 

 

 

Many different solutions possible.

Like a=48, b=96, c=288, d=864, e=4320

Which is larger?

Rich Tasks 68: 2020

2020

Number 2020 - Facts about the integer

Rich Tasks 55: Powers 1

Also look: Different forms of a number

Problem 29: Numbers in circles

The figure shows seven circles joined by three straight lines. The numbers 9, 12, 18, 24, 36, 48 and 96 are to be placed into the circles, one in each so that the product of the three numbers on each of the three lines is the same. Which of the numbers could go in the center?

Source: UKMT