Page 23 - NUMINO Challenge_D2
P. 23
Type 2-2 Finding the Unlocked Locker
All 50 lockers that are numbered 1 to 50 in a classroom are locked.
Each locker belongs to each student numbered 1 to 50. If 50 students
open the locked lockers and lock the opened lockers in the following
ways, write all the locker numbers that are opened.
Student 1 opens all the lockers.
Student 2 locks the lockers numbered with multiples of 2.
Student 3 locks the opened lockers and opens the locked
lockers numbered with multiples of 3.
The rest of the students lock the opened lockers and open
the locked lockers numbered with the multiples of the
student numbers.
1 The following table shows the numbers of the students who opened and
locked each numbered locker. Complete the table.
Locker Number 1 2 3 4 5 6 7 8 9 10
Student
Number
2 What is the relationship between each locker number and the numbers of
students who opened and locked each locker from 1 ?
3 Which lockers from 1 to 10 are opened? Do those numbers have an even
number of factors or an odd number of factors?
4 If an odd number of students open and lock the locker repeatedly, the
locker should be opened at the end. Find the similarity among the
numbers found in 3 that have an odd number of factors.
5 Find all the lockers that are opened by using square numbers from 1 to 50.
20 NUMINO Challenge D2
All 50 lockers that are numbered 1 to 50 in a classroom are locked.
Each locker belongs to each student numbered 1 to 50. If 50 students
open the locked lockers and lock the opened lockers in the following
ways, write all the locker numbers that are opened.
Student 1 opens all the lockers.
Student 2 locks the lockers numbered with multiples of 2.
Student 3 locks the opened lockers and opens the locked
lockers numbered with multiples of 3.
The rest of the students lock the opened lockers and open
the locked lockers numbered with the multiples of the
student numbers.
1 The following table shows the numbers of the students who opened and
locked each numbered locker. Complete the table.
Locker Number 1 2 3 4 5 6 7 8 9 10
Student
Number
2 What is the relationship between each locker number and the numbers of
students who opened and locked each locker from 1 ?
3 Which lockers from 1 to 10 are opened? Do those numbers have an even
number of factors or an odd number of factors?
4 If an odd number of students open and lock the locker repeatedly, the
locker should be opened at the end. Find the similarity among the
numbers found in 3 that have an odd number of factors.
5 Find all the lockers that are opened by using square numbers from 1 to 50.
20 NUMINO Challenge D2
