It is embarrassing to ask people directly for their ages or something related to numbers. Do you mind my asking for your monthly income? I am quite sure you do. Now we are trying to play a game about numbers. You may have tried it before and we may have a great discovery this time.

There are some rows of numbers below.

Row A: 1, 3, 5, 7, 9, 11, 13, 15

Row B: 2, 3, 6, 7, 10, 11, 14, 15

Row C: 4, 5, 6, 7, 12, 13, 14, 15

Row D: 8, 9, 10, 11, 12, 13, 14, 15

John chooses the number of 9 and he does not need to tell it. He just needs to say where it appears. After hearing rows A and D, the first numbers of the two rows are added and the sum is nine. (1 from row A + 8 from row D = 9) Therefore I am sure that he has chosen 9.

7 appears in rows A, B and C. The first numbers (1, 2 and 4) are added and the sum is seven.

Is it tricky? It is not embarrassing to tell you that it is absolutely not tricky.

We do not need to browse through all the numbers at the end of the rows when we want to know the greatest number we can choose. The greatest number a player can choose is 15 because the total of all the first numbers (1, 2, 4 and is 15.

1 is the basic number of this game. Hence 1 must be seen as a first number in a row.

1 x 2 = 2 Hence 2 appears in another row as a first number.

3 is not needed to be a first number in any row because 1 + 2 = 3.

2 x 2 = 4 Hence 4 appears in a row as a first number.

5, 6 and 7 are not needed to be the first numbers in any rows because

1 + 4 = 5 ; 2 + 4 = 6 ; 1 + 2 + 4 = 7

4 x 2 = 8 Hence 8 appears in a row as a first number.

When the first numbers of four rows are calculated, it is easy to know the limit of the game. This can figure out the range of numbers from 1 to 15. After the first number (that is 1) that can be a first number of a row is found, the following first numbers can be worked out soon by doubling the answers. (1 x 2 = 2 ; 2 x 2 = 4 ; 4 x 2 =

1, 2, 4 and 8 are unique and they cannot be the sums of any first numbers of any rows. Thus these four numbers appear once.

9 is 1 and 8 (that is 1+8), so the number 9 appears in rows A and D.

10 is 2 and 8, so the number 10 appears in rows B and D.

11 is 1 and 2 and 8, so the number 11 appears in rows A, B and D.

12 is 4 and 8, so the number 12 appears in rows C and D.

13 is 1 and 4 and 8, so the number 13 appears in rows A, C and D.

14 is 2 and 4 and 8, so the number 14 appears in rows B, C and D.

15 is 1 and 2 and 4 and 8, so the number 15 appears in rows A, B, C and D.

The rows of numbers are not difficult to make when we understand the principle behind. First of all, we have to set the limit. If the total of the first numbers is not greater than one hundred, we cannot be successful to calculate the correct number that is over one hundred. Second, we have to set the first numbers of the rows by doubling the answers as above. The more first numbers are set, the more rows of numbers are made. The limit of numbers for players to choose within is also increased in this condition. Third, we need to arrange other numbers to follow the first numbers. The other numbers are the numbers that would not overlap with the first numbers. The first numbers of the rows never appear more than once and other numbers always appear more than once.

Is it interesting? It is not embarrassing to tell you that it is absolutely interesting. Before asking people for sensitive numbers, it is necessary to make some complete rows of numbers. We do not need to ask for their ages for example directly. We just need them to answer us yes when their number appears in a row or no when their number does not appear in a row. After showing them the rows of numbers one by one without repetition and obtaining the answers of yes and no, we can calculate the numbers we want from them by adding all the first numbers of the rows they claim yes. There are more mysterious numbers and mathematical magic (MM) at seekingmydear.110mb.com.

Now I have a task for you. Try to make some rows of numbers that can calculate how many marks a student scores in a test. The full mark is assumed to be one hundred. Please write down the rows on the comment zone as soon as possible (ASAP) because you may have a free ticket to my workshop if the numbers are not wrong. Come on, action!