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# A Bingo Card Puzzle (A very lengthy math puzzle)

### #1

Posted 20 June 2012 - 02:19 PM

[1] On the cards, there are five columns (named hereafter as A, B, C, D, & E) and five rows (named hereafter as J, K, L, M, & N).

[2] Column 'A' contains numbers 1 through 15.

[3] Column 'B' contains numbers 16 through 30.

[4] Column 'C' contains numbers 31 through 45.

[5] Column 'D' contains numbers 46 through 60.

[6] Column 'E' contains numbers 61 through 75.

[7] Center space 'CL' (a place in column C and row L) is free space i.e. contains no number.

[8] In row 'J', each numeral (0 through 9) appears only once; e.g. if there is number 43 at space DJ, then at other spaces in this row, there would be no number containing numeral 3 & 4.

[9] In row M, sum of all numbers is a perfect square.

[10] Row N contains the smallest number in each column.

[11] Each row contains only one '2-digit Prime Number'.

[12] In column C, difference of lowest to highest number is 8.

[13] In column D, each number has digit at 10th place smaller than the digit at unit place.

[14] In column E each number is an odd number.

[15] In only one column, the numbers are in descending order from top to bottom.

[16] In each column, there is only one numeral that appears two times.

[17] In each column, the sum of numbers shares a single common prime factor.

[18] On the bingo card, numeral 5 appears only once.

[19] The sum of the numbers in each diagonal is an odd number.

[20]The product of numbers at spaces AL & EL has a unit digit 2.

[21] The product of numbers at spaces BL & DL has a unit digit 4.

### #2

Posted 20 June 2012 - 07:57 PM

Do bingo cards have a specific amount of numbers on them?

hi again, everyone. Nice to be back home.

### #3

Posted 21 June 2012 - 02:26 AM

I'm not sure about the reference to a stack of cards.

Nowhere does it say that at least one crd in the stack has the required array of numbers.

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #4

Posted 21 June 2012 - 03:24 PM

You are right. The puzzle is to create a 5X5 array of numbers that satisfy the given clues.I'm guessing that the puzzle is to create a 5x5 array of numbers that satisfy the clues.

I'm not sure about the reference to a stack of cards.

Nowhere does it say that at least one crd in the stack has the required array of numbers.

It is a lenghthy math puzzle requires lot patience.

### #5

Posted 21 June 2012 - 03:30 PM

Solution is not concerned to a bingo card, or stack. One is required to creat a 5X5 table containing numbers as per the clues given.Well that's easy (not)

Do bingo cards have a specific amount of numbers on them?

### #6

Posted 21 June 2012 - 03:36 PM

hi again, everyone. Nice to be back home.

### #7

Posted 21 June 2012 - 04:05 PM

You are right....!So we need 24 numbers because 'CL' is the only blank.

### #8

Posted 21 June 2012 - 08:06 PM

No two Boxes contain the same number?

8. Once and only once?

15. One and only one column?

16. Do you mean exactly two times? To prohibit having 2 sixes and 3 eights?

17. The five column sums share one and only one prime factor?

18. Once and only once?

Then, if CL is 45 then 50-59 do not appear in col D?

19. Major diagonal?

Thanks.

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #9

Posted 21 June 2012 - 11:09 PM

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #10

Posted 22 June 2012 - 12:01 AM

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