2. Nine Card solitaire In this game of solitaire, each of the 9 cards has a one-

Question

2. Nine Card solitaire In this game of solitaire, each of the 9 cards has a one-digit number on the side that is turned down. Numbers 1-9 appear on the cards. The numbers of the 4 corner cards are odd numbers. Row 1 contains 3 consecutive odd numbers. One of the diagonals contains prime factors of 84. Numbers in row 1 are factors of 30. Numbers in column 1 are factors of 72. The column 3 total is twice the row 1 total. The column 1 total is equal to the row 3 total. Tell what digit is on each card.

Explanation / Answer

Solution

For easy in explaining, let us number the given conditions.

Numbers in 4 corner cards are odd numbers. ………........................................…. (1)

Row 1 contains 3 consecutive odd numbers……………......................................... (2) [Note that the question does not say that these are in order]

One of the diagonals contains prime factors of 84, i.e., 2, 3 and 7 ...................……. (3)

Numbers in Row 1 are factors of 30, i.e., 1, 2, 3, 5, 6 ……...................................... (4)

Numbers in Column 1 are factors of 72, i.e., 1, 2, 3, 4, 6, 8 ..............................…… (5)

Column 3 total = 2 x Row 1 total ............................................................................(6)

Column 1 total = Row 3 total …….......................................................................... (7)

Now,

(1) and (3) => 2 is in the central position …..........................................................… (8)

(4) and (5) => 7 can neither be in Row 1 nor in Column 1 ….....................................… (9)

(8) and (9) => 7 must be at the last position, i.e., 3rd row-3rd column …..................... (10)

(10) and (3) => 3 must be at the first position, i.e., 1st row-1st column ….................... (11)

(11) and (2) => Row 1 has 3 1 5 or 3 5 1 in either order [in both cases, sum is 9 …….. (12)

(6) and (12) => Column 3 has 5, 6, 7 in that order and hence Row 1 is 3 1 5 ….........…(13)

(11), (10) and (7) => Column 1 is 3 8 9 and Row 3 is 9 4 7.

Thus, the numbers’ position are as shown below:

Row 1:   3    1    5

Row 2;   3    2   6

Row 3: 9    4    7 ANSWER

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