Page 97 - NUMINO Challenge_C1

11 Rules of Arrangements

Basic Concepts Rules of Sequences with Quotients and Remainders

When arranging numbers in a table following a certain rule, you can find a
pattern in the numbers of each column and row.

Quotient 0 1 234
0 4 8 12 16
Remainder

0

1 1 5 9 13 17 Numbers that have the same remainder when
divided by 4.

2 2 6 10 14 18

3 3 7 11 15 19

Numbers that have the same quotient
when divided by 4.

Example Numbers are written one by one clockwise next to the five vertices
of a pentagon. At which place and vertex will 96 be written?

11

6

1

A

15 10 5 E B 2 7 12

D C
94 3
14 8 13

Class Notes

When divided by 5, the numbers written next to vertices A , B , C , D , and E
have remainders 1, , , , and , respectively.

Since 96 has a remainder of when divided by 5, it is written next to vertex .

Since 1 has a quotient of when divided by 5, it is written in the 1st place next

to point . Since 6 has a quotient of when divided by 5, it is written in the th

place.

Likewise, since 96 has a quotient of when divided by 5, it will be written in the

th

place.

94 NUMINO Challenge C1