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

18 replies to this topic

### #1 bhramarraj

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Posted 20 June 2012 - 02:19 PM

There is a stack of Bingo Cards. It is required to find a specific card having the number arrangement as hinted in the following clues:
[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.
• 1

### #2 MikeD

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Posted 20 June 2012 - 07:57 PM

Well that's easy (not)

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

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Posted 21 June 2012 - 02:26 AM

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.
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### #4 bhramarraj

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Posted 21 June 2012 - 03:24 PM

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.

You are right. The puzzle is to create a 5X5 array of numbers that satisfy the given clues.
It is a lenghthy math puzzle requires lot patience.
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### #5 bhramarraj

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Posted 21 June 2012 - 03:30 PM

Well that's easy (not)

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

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.
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### #6 MikeD

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Posted 21 June 2012 - 03:36 PM

So we need 24 numbers because 'CL' is the only blank.
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### #7 bhramarraj

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Posted 21 June 2012 - 04:05 PM

So we need 24 numbers because 'CL' is the only blank.

You are right....!
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### #8 bonanova

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Posted 21 June 2012 - 08:06 PM

Clarifications.

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.
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### #9 bonanova

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Posted 21 June 2012 - 11:09 PM

Spoiler for first steps

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### #10 superprismatic

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Posted 22 June 2012 - 12:01 AM

Spoiler for what I have so far

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