Page 162 - NUMINO Challenge_B1
P. 162
Problem solving Problem solving
1 The number of squares in arrangements , , and 1 The numbers of line segments in the first three
are 1, 5, and 13, respectively. Divide the squares steps are 1, 4, and 16. These values can be
into two parts. The number of these squares can expressed as 1, 1 4, and 4 4.
be expressed as (0 0) (1 1), (1 1) (2 2), and Therefore, 4 4 4 64 line segments are
(2 2) (3 3). Therefore the nth arrangement will drawn in Step 4.
have (n 1) (n 1) (n n) squares. In the sixth
arrangement, there will be (5 5) (6 6) 61 2 The number of circles in the first three steps are
squares.
1, 3, and 7. These values can be expressed as 1,
2 The numbers of matches used in the first four 1 2, and 1 2 (2 2). Therefore, there will be
1 2 (2 2) (2 2 2) 15 circles in Step 4.
steps are 4, 12, 24, and 40. These values can be
expressed as (1 2) 2, (2 3) 2, (3 4) 2, and Creative Thinking p.100~p.101
(4 5) 2.
So the nth arrangement has n (n 1) 2 matches. 1 The numbers of matches needed to make the
Therefore, you will need (6 7) 2 84 matches
in Step 6. 1st, 2nd, 3rd, and 4th arrangements are 4, 10, 18,
and 28, respectively. These values can be
Type 11-2 Increase in Number by Multiplication p.98~p.99 expressed as 1 4, 2 5, 3 6, and 4 7. So the
nth arrangement has n (n 3) matches.
1 9 branches Therefore, 6 9 54 matches are needed for
the sixth arrangement.
2 Step 4: 27 branches.
2 The numbers of flowers in the 1st, 2nd, 3rd, and
3 Step 1 Step 2 Step 3 Step 4
4th arrangements are 2, 8, 18, and 32
respectively. Divide each arrangement in two
equal parts. The number of flowers in each
arrangement can be expressed as
(1 1) 2, (2 2) 2, (3 3) 2, and (4 4) 2.
Therefore, there will be (5 5) 2 50 flowers in
the fifth arrangement.
Number of 1 3 9 27
Branches
333
4 27 3 81 branches
Answer Key
1 The number of squares in arrangements , , and 1 The numbers of line segments in the first three
are 1, 5, and 13, respectively. Divide the squares steps are 1, 4, and 16. These values can be
into two parts. The number of these squares can expressed as 1, 1 4, and 4 4.
be expressed as (0 0) (1 1), (1 1) (2 2), and Therefore, 4 4 4 64 line segments are
(2 2) (3 3). Therefore the nth arrangement will drawn in Step 4.
have (n 1) (n 1) (n n) squares. In the sixth
arrangement, there will be (5 5) (6 6) 61 2 The number of circles in the first three steps are
squares.
1, 3, and 7. These values can be expressed as 1,
2 The numbers of matches used in the first four 1 2, and 1 2 (2 2). Therefore, there will be
1 2 (2 2) (2 2 2) 15 circles in Step 4.
steps are 4, 12, 24, and 40. These values can be
expressed as (1 2) 2, (2 3) 2, (3 4) 2, and Creative Thinking p.100~p.101
(4 5) 2.
So the nth arrangement has n (n 1) 2 matches. 1 The numbers of matches needed to make the
Therefore, you will need (6 7) 2 84 matches
in Step 6. 1st, 2nd, 3rd, and 4th arrangements are 4, 10, 18,
and 28, respectively. These values can be
Type 11-2 Increase in Number by Multiplication p.98~p.99 expressed as 1 4, 2 5, 3 6, and 4 7. So the
nth arrangement has n (n 3) matches.
1 9 branches Therefore, 6 9 54 matches are needed for
the sixth arrangement.
2 Step 4: 27 branches.
2 The numbers of flowers in the 1st, 2nd, 3rd, and
3 Step 1 Step 2 Step 3 Step 4
4th arrangements are 2, 8, 18, and 32
respectively. Divide each arrangement in two
equal parts. The number of flowers in each
arrangement can be expressed as
(1 1) 2, (2 2) 2, (3 3) 2, and (4 4) 2.
Therefore, there will be (5 5) 2 50 flowers in
the fifth arrangement.
Number of 1 3 9 27
Branches
333
4 27 3 81 branches
Answer Key
