Page 11 - NUMINO Challenge_B1

1 Number Arrangement Puzzles

Basic Concepts How Many Numbers Are there Between Two Numbers?

Six number cards are arranged as follows:
One number card is placed between the 1’s, two number cards are placed
between the 2’s, and three number cards are placed between the 3’s.

231213

In a puzzle like this, the greater the number, the fewer possible ways you
can arrange the numbers. Therefore, you should start with the greater
numbers.

Placing 1’s Placing 2’s Placing 3’s
Four possible ways Three possible ways Two possible ways

11 22 33

11 22 33

11 22

11

Example Two 1’s, 2’s, 3’s, and 4’s are given. Try to arrange the eight
numbers with the rules given above.

or

Class Notes

When there are two 1’s, 2’s, 3’s, and 4’s, you can place four

numbers between two 4’s in way(s). For each way, there is/are

way(s) to place three numbers between two 3’s.

44 44 44

43 43 4 4 44
4 4 44
4 343

If you try to place the numbers in each arrangement starting with 4’s, you will find
that there are two different ways to place two numbers between two 2’s and one
number between two 1’s. The two ways are as follows:

43 43

8 NUMINO Challenge B1