Page 147 - NUMINO Challenge_D2
P. 147
Answer Problem solving
Key
1 If you divide the space inside the fence into nine
Reasoning
partitions and put one sheep in each partition,
4 Principle of Drawers p.34~p.35 then one sheep will be left outside. If you put
the remaining sheep in one of the nine
Example 6, 6 2, 5 5 partitions, then one partition will have two
sheep. Therefore, there are two sheep that are
Example 4 3 2, 1 10 located within a distance closer to 5 m, and
therefore A is correct.
TryItAgain If Lisa stamps four different stamps and
stamp ‘e’ is not stamped, then the last 2 There are eight pairs of number cards that have
stamp is stamp ‘e’. The remaining stamps
should be stamped three times, two times, a difference of 12: (1, 13), (2, 14), (3, 15), (4, 16),
and once, and since the letter on the last (5, 17), (6, 18), (7, 19), and (8, 20). The students
stamp can be guessed, it doesn't need to be who cannot be taggers are those who have the
stamped. Therefore, the stamps need to be number card 9, 10, 11, or 12. If these four
stamped at least 4 3 2 1 10 times. students, one student from each of the eight
pairs of people, has a number difference of 12,
Type 4-1 Picking the Card You Need p.36~p.37 and another student is picked, then the taggers
can be chosen. Therefore, at least 4 8 1 13
1 Starting from 1, find the pairs of numbers that students must be chosen.
have a difference of 18.
(2, 20), (3, 21), (4, 22), (5, 23), (6, 24), (7, 25), Type 4-2 Number of Votes Obtained p.38~p.39
(8, 26), (9, 27), (10, 28), (11, 29), (12, 30)
1 Since the total number of votes Dan, Sophie,
2 13, 14, 15, 16, 17, 18 and Jane obtained is 10 16 7 33 (votes),
then there are 50 33 17 votes that are not
3 Take out one card from each of the 12 pairs of cast yet.
the cards that have a difference of 18, and pick
one more card from the remaining cards. 2 Since Dan has more votes than Jane, therefore
Therefore, 12 1 13 cards need to be taken the unfavorable situation for Sophie is that Dan
out. gets all the votes Sophie cannot get.
4 Think about the unluckiest case. First, take out 3 From the remaining 17 votes, if Sophie gets five
six cards that cannot be paired. Then, take out votes, Dan gets 12 votes, then Sophie will get at
one card from each of the twelve pairs of the total of 16 5 21 votes, and Dan will get a
cards that have a difference of 18. At the end, total of 10 12 22 votes. Therefore Dan will be
take out one more card, and then you will have selected as the class president. If Sophie gets six
one pair of cards that have a difference of 18. votes and Dan gets 11 votes, then Sophie will
Therefore, at least 6 12 1 19 cards need to get a total of 16 6 22 votes, and Dan will get
be taken out. a total of 10 11 21 votes. Therefore, Sophie
will be selected as the class president.
Therefore, Sophie needs to get at least 6 more
votes.
NUMINO Challenge D2
Key
1 If you divide the space inside the fence into nine
Reasoning
partitions and put one sheep in each partition,
4 Principle of Drawers p.34~p.35 then one sheep will be left outside. If you put
the remaining sheep in one of the nine
Example 6, 6 2, 5 5 partitions, then one partition will have two
sheep. Therefore, there are two sheep that are
Example 4 3 2, 1 10 located within a distance closer to 5 m, and
therefore A is correct.
TryItAgain If Lisa stamps four different stamps and
stamp ‘e’ is not stamped, then the last 2 There are eight pairs of number cards that have
stamp is stamp ‘e’. The remaining stamps
should be stamped three times, two times, a difference of 12: (1, 13), (2, 14), (3, 15), (4, 16),
and once, and since the letter on the last (5, 17), (6, 18), (7, 19), and (8, 20). The students
stamp can be guessed, it doesn't need to be who cannot be taggers are those who have the
stamped. Therefore, the stamps need to be number card 9, 10, 11, or 12. If these four
stamped at least 4 3 2 1 10 times. students, one student from each of the eight
pairs of people, has a number difference of 12,
Type 4-1 Picking the Card You Need p.36~p.37 and another student is picked, then the taggers
can be chosen. Therefore, at least 4 8 1 13
1 Starting from 1, find the pairs of numbers that students must be chosen.
have a difference of 18.
(2, 20), (3, 21), (4, 22), (5, 23), (6, 24), (7, 25), Type 4-2 Number of Votes Obtained p.38~p.39
(8, 26), (9, 27), (10, 28), (11, 29), (12, 30)
1 Since the total number of votes Dan, Sophie,
2 13, 14, 15, 16, 17, 18 and Jane obtained is 10 16 7 33 (votes),
then there are 50 33 17 votes that are not
3 Take out one card from each of the 12 pairs of cast yet.
the cards that have a difference of 18, and pick
one more card from the remaining cards. 2 Since Dan has more votes than Jane, therefore
Therefore, 12 1 13 cards need to be taken the unfavorable situation for Sophie is that Dan
out. gets all the votes Sophie cannot get.
4 Think about the unluckiest case. First, take out 3 From the remaining 17 votes, if Sophie gets five
six cards that cannot be paired. Then, take out votes, Dan gets 12 votes, then Sophie will get at
one card from each of the twelve pairs of the total of 16 5 21 votes, and Dan will get a
cards that have a difference of 18. At the end, total of 10 12 22 votes. Therefore Dan will be
take out one more card, and then you will have selected as the class president. If Sophie gets six
one pair of cards that have a difference of 18. votes and Dan gets 11 votes, then Sophie will
Therefore, at least 6 12 1 19 cards need to get a total of 16 6 22 votes, and Dan will get
be taken out. a total of 10 11 21 votes. Therefore, Sophie
will be selected as the class president.
Therefore, Sophie needs to get at least 6 more
votes.
NUMINO Challenge D2
