Twelve cards in which the numbers from 1 to 12 were written are put in order like #1 in a figure at first.
In accordance with the same rule, it rearranges with #2, #3, #4, and .... after that.
Answer each of following questions.
(1) Fill in the blank of #5 in a figure.
(2) Find the number which is to be the same as #1 for the first time after #2.
(3) Fill in the blank of #2006 in a figure.
According to #1 and #2, 1~6 in the left column rearranged every other one and 7~12 in the right column is put between them.
Thinking it more briefly, as shown in a figure, 7~12 are put among 1~6 of a left column and all of them are rearranged.
Based on this rule, #5 is come out by rearranging #4.
(2) It would be better to rearrange in order by yourself until it comes to be the same as #1.
It is #11 to become the same as #1 as shown in a figure.
Therefore, 2006 / 10 = 200 remainder 6.
This outcome means that #2006 comes to be the same as #6.
In accordance with the same rule, it rearranges with #2, #3, #4, and .... after that.
Answer each of following questions.
(1) Fill in the blank of #5 in a figure.
(2) Find the number which is to be the same as #1 for the first time after #2.
(3) Fill in the blank of #2006 in a figure.
Answer
(1)
(2) #11
(3)
Solution
(1) The rule of rearrangement of the cards should be confirmed. According to #1 and #2, 1~6 in the left column rearranged every other one and 7~12 in the right column is put between them.
Thinking it more briefly, as shown in a figure, 7~12 are put among 1~6 of a left column and all of them are rearranged.
Based on this rule, #5 is come out by rearranging #4.
(2) It would be better to rearrange in order by yourself until it comes to be the same as #1.
It is #11 to become the same as #1 as shown in a figure.
(3) According to (2), since #1, #11, #21, and #31 comes to be the same, it turns out that the cycle which comes to be the same is 10.
Therefore, 2006 / 10 = 200 remainder 6.
This outcome means that #2006 comes to be the same as #6.
