### Brain Teasers

# Bingo Card 4

You are given a stack of bingo cards. Your task is to find a specific card. Given the following clues, what is the number arrangement of that card?

Columns, left to right, are: B (contains numbers 1 through 15), I (contains numbers 16 through 30), N (contains numbers 31 through 45), G (contains numbers 46 through 60), O (contains numbers 61 through 75). Rows, top to bottom, are: 1, 2, 3, 4, 5. An example of coordinate nomenclature: B1 identifies column B row 1. N3 is a free space (contains no number). No number appears more than once.

1) Each numeral (0 through 9) appears one time in Row 1.

2) The sum of the numbers in Row 4 is a square number.

3) There is only one two-digit prime number in each row.

4) The range of the numbers in Column N is 8.

5) Each number in Column G has a tens digit that is less than the units digit.

6) Each number in Column O is odd.

7) In only one column are the numbers in descending order from top to bottom.

8) Each column has only one numeral that appears exactly two times.

9) The smallest number in each column is located in Row 5.

10) The sums of each column share a single common prime factor.

11) The numeral 5 only appears one time on the card.

12) The sum of the numbers in each diagonal is an odd number.

13) The product of B3 and O3 has a units digit of 2.

14) The product of I3 and G3 has a units digit of 4.

Columns, left to right, are: B (contains numbers 1 through 15), I (contains numbers 16 through 30), N (contains numbers 31 through 45), G (contains numbers 46 through 60), O (contains numbers 61 through 75). Rows, top to bottom, are: 1, 2, 3, 4, 5. An example of coordinate nomenclature: B1 identifies column B row 1. N3 is a free space (contains no number). No number appears more than once.

1) Each numeral (0 through 9) appears one time in Row 1.

2) The sum of the numbers in Row 4 is a square number.

3) There is only one two-digit prime number in each row.

4) The range of the numbers in Column N is 8.

5) Each number in Column G has a tens digit that is less than the units digit.

6) Each number in Column O is odd.

7) In only one column are the numbers in descending order from top to bottom.

8) Each column has only one numeral that appears exactly two times.

9) The smallest number in each column is located in Row 5.

10) The sums of each column share a single common prime factor.

11) The numeral 5 only appears one time on the card.

12) The sum of the numbers in each diagonal is an odd number.

13) The product of B3 and O3 has a units digit of 2.

14) The product of I3 and G3 has a units digit of 4.

### Answer

10 24 39 58 679 28 40 49 71

8 22 -- 47 69

3 30 42 48 73

1 20 34 46 61

1) Per clue 5, eliminate the appropriate numbers in Column G. Of the remaining numbers, at least one with a tens digit of 5 will have to be used. Per clues 1 and 11, only one number can have the numeral 5, so that number must be at G1. Eliminate all numbers that contain a 5 from all other locations.

2) Per clue 6, eliminate all even numbers from Column O.

3) Per clue 1, eliminate any number from Row 1 with only one digit or duplicate digits. By analyzing combinations of numbers, the following can be determined: B1 contains a 1, delete 30, I1 contains a 2, delete 23, delete 63 and 73, O1 contains a 6. In conjunction with clue 3, delete 29 and 59.

4) Per clue 10, analyze the various possible sums of Columns G and O. The only common prime factor is 31. Each column must sum to a multiple of 31 (based on available numbers: B to 31, I to 124, N to 155, G to 248, and O to 341). G1 must be 58. All two-digit prime numbers (clue 3) must be in Columns G and O. O1 must be 67. Per clue 1, N1 must be 39. Per clue 9, G5 must be 46 and O5 must be 61.

5) For Column N, there is only set of numbers that sums to 155, and satisfies clues 4, 8, and 9 (34, 39, 40, 42). N5 must be 34.

6) For Column I, there are two sets of numbers that sum to 124, and satisfy clues 8 and 9 (16, 24, 26, 28, 30 and 20, 22, 24, 28, 30). To satisfy clue 1, I1 must be 24. B1 must be 10. To satisfy clue 12, G4 must be 48 and B5 must be odd.

7) The column that satisfies clue 7 is Column B. To satisfy clue 8, B2 must be 9 and B5 must be 1.

8) To satisfy clue 2, the only square number that can be achieved is 196. B4 must be 3, I4 must be 30, N4 must be 42, and O4 must be 73.

9) B3 must be 8. N2 must be 40.

10) To satisfy clue 13, O3 must be 69. This leaves O2 being 71. To satisfy clue 3, G3 must be 47. This leaves G2 being 49.

11) To satisfy clue 14, I3 must be 22. Finally, to achieve a sum of 124 (multiple of 31), I2 must be 28 and I5 must be 20.

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