### Brain Teasers

# Bingo Card

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) All numbers in row 2 are divisible by 2; all numbers in row 3 are divisible by 3; all numbers in row 4 are divisible by 4; all numbers in row 5 are divisible by 5.

2) Row 2: the units digits are the same.

3) Row 4: the units digits are all different.

4) Row 5: the sum of the numbers is divisible by 7.

5) Column B: contains five consecutive numbers (in any order).

6) Column I: three of the numbers are odd.

7) Column G: three numbers are divisible by 3; three numbers are divisible by 4; one number is divisible by 12.

8) Column O: the sum of the five numbers is an odd number.

9) The product of I3 and G3 is between 1300 and 1400.

10) The sum of B1 and O1 is 82.

11) The difference between N1 and N5 is 1.

12) N2 is midway between B4 and O4.

13) N4 is midway between I1 and G1.

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) All numbers in row 2 are divisible by 2; all numbers in row 3 are divisible by 3; all numbers in row 4 are divisible by 4; all numbers in row 5 are divisible by 5.

2) Row 2: the units digits are the same.

3) Row 4: the units digits are all different.

4) Row 5: the sum of the numbers is divisible by 7.

5) Column B: contains five consecutive numbers (in any order).

6) Column I: three of the numbers are odd.

7) Column G: three numbers are divisible by 3; three numbers are divisible by 4; one number is divisible by 12.

8) Column O: the sum of the five numbers is an odd number.

9) The product of I3 and G3 is between 1300 and 1400.

10) The sum of B1 and O1 is 82.

11) The difference between N1 and N5 is 1.

12) N2 is midway between B4 and O4.

13) N4 is midway between I1 and G1.

### Answer

7 23 44 57 756 26 36 56 66

9 27 -- 51 72

8 16 40 52 64

10 25 45 60 70

1) Per clue 1, eliminate the appropriate numbers in the various rows.

2) Per clue 6, since rows 2 and 4 must contain even numbers, the other three rows in column I must contain odd numbers. I5 must be 25.

3) Per clue 7, G5 must be 60.

4) Per clue 9, I3 must be 27 and G3 must be 51.

5) Per clue 13, since I1 is odd, then G1 must be odd. G1 must be 57. I1 must be 23. N4 must be 40.

6) Per clue 10, B1 can not be less than 7 and O1 can not be less than 67.

7) Per clue 2, based on G2, no number in row 2 can end in 0 or 4 or 8.

8) Per clue 5, eliminate impossible combinations in column B.

9) Per clue 12, eliminate numbers that can not work. N2 must be 36. O4 must be either 64 or 68.

10) Per clue 2, the units digits is 6. B2 must be 6. G2 must be 56. O2 must be 66. This leaves G4 as 52.

11) Per clue 5, eliminate impossible combinations in column B. B1 must be 7.

12) Per clue 10, O1 must be 75.

13) Per clue 3, I4 must be 16. This leaves I2 as 26.

14) Per clue 4, in order for the sum of row 5 to be divisible by 7, the sum must be either 175 or 210. Since I5 must be 25 and G5 must be 60, then the sum must be 210. B5 must be 10. N5 must be 45. O5 must be 70.

15) Per clue 5, B3 must be 9 and B4 must be 8.

16) Per clue 3, O4 must be 64.

17) Per clue 8, O3 must be 72.

18) Per clue 11, N1 must be 44.

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