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## Bingo Card 3

Logic puzzles require you to think. You will have to be logical in your reasoning.

 Puzzle ID: #44758 Fun: (2) Difficulty: (2.72) Category: Logic Submitted By: cnmne

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) For each column, the numbers are in either ascending order or descending order.
2) Row 1: the numbers are prime.
3) Row 5: the numbers are composite.
4) Column I: the numbers are spaced at equal intervals.
5) Column O: the numbers are spaced at different intervals.
6) The sum of the numbers in Row 1 equals the sum of the numbers in Row 5.
7) The product of B4 and O5 equals the product of B5 and O4.
8) The product of I2 and G2 equals the product of I3 and G3.
9) N4 is midway between B4 and G4.
10) Each column has one multiple of 6.
11) There is only one square number on the card.

11 17 41 59 61
12 18 36 57 63
13 19 -- 54 66
14 20 33 52 70
15 21 32 46 75

1) Per clue 2, eliminate non-prime numbers from Row 1.
2) Per clue 3, eliminate non-composite numbers from Row 5.
3) Per clue 1, eliminate numbers that do not fit any possible (ascending or descending) sequence from Rows 2 through 4.
4) Per clue 4, determine the possible sequences for Column I. In conjunction with clue 8, eliminate numbers from Columns I and G.
5) Per clue 10, I2 must be 18 or 24, and G3 must be 48 or 54. Eliminate additional numbers from Column G.
6) Per clue 7, determine what combinations of numbers work. Eliminate those that to not work from B4, B5, O4, and O5.
7) Per clue 5, in order to have four different intervals, the spread from top to bottom must be at least 10. Eliminate from O1: 67 and 71. Eliminate from O5: 64 and 70. In conjunction with clue 7, only one combination of numbers works: O4 must be 70, O5 must be 75, B4 must be 14, and B5 must be 15. This leaves O1 as 61.
8) Per clue 10, 66 must be in either O2 or O3. 66 can not be in O2, because that would create an interval of 5 (which already exists between O4 and O5) between O1 and O2. O3 must be 66. O2 must be either 63 or 64.
9) Per clue 9, N4 must be 33 and G4 must be 52. This leaves G1 as 59, G2 as 57, and G3 as 54.
10) Per clues 4 and 8, Column I can be determined. I1 must be 17, I2 must be 18, I3 must be 19, I4 must be 20, and I5 must be 21.
11) Per clue 6, Column N must be in descending order. N5 must be 32.
12) Per clue 6, the only combination of numbers that works produces a sum of 189. B1 must be 11, N1 must be 41, G5 must be 46.
13) Per clue 1, B2 must be 12 and B3 must be 13.
14) Per clue 10, N2 must be 36. Per clue 11, O2 must be 63.

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