### Brain Teasers

# Bingo Card 2

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) Row 1: the tens digits are all different.

2) Row 2: the numbers are even.

3) Row 4: the sum of the five numbers is 178.

4) Row 5: the numbers are prime.

5) Column B: the sum of the five numbers is 60.

6) Column I: two of the numbers are greater than 19.

7) Column O: the numbers are in increasing equally-spaced order, from top to bottom.

8) The product of B3 and O3 is between 600 and 700.

9) The sum of I1 and G5 equals the sum of G1 and I5.

10) N1 is midway between I4 and G4.

11) N5 is midway between I2 and G2.

12) I3 is midway between B1 and N1, and G3 is midway between N1 and O1.

13) There are five numbers that are divisible by 11; only one per row and one per column.

14) There is one triangle number in each column.

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) Row 1: the tens digits are all different.

2) Row 2: the numbers are even.

3) Row 4: the sum of the five numbers is 178.

4) Row 5: the numbers are prime.

5) Column B: the sum of the five numbers is 60.

6) Column I: two of the numbers are greater than 19.

7) Column O: the numbers are in increasing equally-spaced order, from top to bottom.

8) The product of B3 and O3 is between 600 and 700.

9) The sum of I1 and G5 equals the sum of G1 and I5.

10) N1 is midway between I4 and G4.

11) N5 is midway between I2 and G2.

12) I3 is midway between B1 and N1, and G3 is midway between N1 and O1.

13) There are five numbers that are divisible by 11; only one per row and one per column.

14) There is one triangle number in each column.

### Answer

13 21 31 55 6312 18 44 56 64

10 22 -- 47 65

14 16 36 46 66

11 19 37 53 67

1) Per clue 2, eliminate the odd numbers in row 2.

2) Per clue 4, eliminate the non-prime numbers in row 5.

3) Per clue 14, 55 must be in column G and 66 must be in column O.

4) Per clue 7, column O must contain 63 through 67, in order, from top to bottom.

5) Per clue 8, B3 must be 10 (a triangle number).

6) Per clue 14, eliminate the following numbers from column B: 1, 3, 6, and 15.

7) Per clue 5, eliminate numbers less than 10.

8) Per clue 12, eliminate impossible combinations.

9) Per clue 13, G1 must be 55. B1 can not be 11, therefore B1 must be 13 and B5 must be 11.

10) Per clue 1, I1 must be greater than 19. Per clue 9, I1 must be 21 or 25 or 27. Per clue 13, 22 must be in column I. Per clue 14, 21 or 28 must be in column I. Per clue 6, only two numbers in column I can be greater than 19. I1 must be 21 and I3 must be 22.

11) Per clue 12, N1 must be 31 and G3 must be 47.

12) Per clue 13, N2 must be 44.

13) Per clue 9, I5 must be 19 and G5 must be 53.

14) Per clue 10, I4 must be 16 and N4 must be 46. This leaves I2 as 18.

15) Per clue 11, N5 must be 37 and G2 must be 56.

16) Per clue 14, N4 must be 36 or 45. Per clue 3, since the sum is even, N4 must be 36. B4 must be 14. This leaves B2 as 12.

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## Comments

It took me a couple of days to do this, but it was entertaining.

It would have to take several days to figure this out, the logic of it all. I myself cannot compute this type of mathematical logic to paper, but to those of you who can, good luck. good work.

I did this one when it was in the review queue. It took over twenty minutes, but I did finally get it.

Very nicely done!

Very nicely done!

Am I missing something? The first clue says all ten digits are different...that would negate the clue that says that each row and column contains a number divisible by 11...

The answer shows that this is not the case...help!

The answer shows that this is not the case...help!

never mind...yep, I can read!

What is a triangle number?

A triangle number is the number of items it takes to make a triangle:

. o = 1

. o

.o o = 3

. o

. o o

. o o o = 6

... 10, 15, 21, 28, 36, 45, 55, 66, ...

. o = 1

. o

.o o = 3

. o

. o o

. o o o = 6

... 10, 15, 21, 28, 36, 45, 55, 66, ...

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