### Brain Teasers

# Class Photo 3

Stacey's class picture has 35 photos arranged in a 7 x 5 grid. The photos in the top row are numbered 1 through 7 from left to right, with the photos in the remaining rows similarly numbered. Given the following clues (bordering includes horizontal, vertical, and diagonal), where is Stacey's picture?

X X X X X X X (1 - 7)

X X X X X X X (8 - 14)

X X X X X X X (15 - 21)

X X X X X X X (22 - 28)

X X X X X X X (29 - 35)

1) Stacey and her two best friends, Rhonda and Teresa, are located along a straight line (horizontally, vertically, or diagonally). However, Stacey does not border either Rhonda or Teresa.

2) The sum of the three positions (Stacey, Rhonda, and Teresa) is a prime number.

3) There are 18 boys and 17 girls.

4) Boys are not located at positions that are square numbers or cube numbers.

5) Girls are not located at positions that are prime numbers.

6) The sum of the positions where boys are located is less than the sum of the positions where girls are located.

7) There are no more than four girls in any row.

8) There are at least two girls in each column.

9) There are no more than three girls in any diagonal.

X X X X X X X (1 - 7)

X X X X X X X (8 - 14)

X X X X X X X (15 - 21)

X X X X X X X (22 - 28)

X X X X X X X (29 - 35)

1) Stacey and her two best friends, Rhonda and Teresa, are located along a straight line (horizontally, vertically, or diagonally). However, Stacey does not border either Rhonda or Teresa.

2) The sum of the three positions (Stacey, Rhonda, and Teresa) is a prime number.

3) There are 18 boys and 17 girls.

4) Boys are not located at positions that are square numbers or cube numbers.

5) Girls are not located at positions that are prime numbers.

6) The sum of the positions where boys are located is less than the sum of the positions where girls are located.

7) There are no more than four girls in any row.

8) There are at least two girls in each column.

9) There are no more than three girls in any diagonal.

### Answer

A) Boys are located at the following positions (clue 5): 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31. Girls are located at the following positions (clue 4): 1, 4, 8, 9, 16, 25, and 27.B) A boy must be at position 33 (clue 9). Girls must be at positions 10, 24, 12, and 26 (clue 8).

C) Boys must be at positions 14, 22, and 28 (clue 7). A boy must be at position 32 (clue 9).

D) Two boys still need to be placed. To satisfy clue 9, they must be among the following three positions: 6, 18, and 30. The summation of all positions (1 through 35) is 630. To satisfy clue 6, the sum of the positions for boys must be less than one-half of 630, or less than 315. The 15 boys already placed have a position sum of 289. To satisfy clue 6, the remaining two boys must add no more than 25. This means that the last two boys must be placed at positions 6 and 18, producing a total of 313. Girls occupy the remaining positions (15, 20, 21, 30, 34, and 35).

Step A Step B Step C Step D

GBBGBxB GBBGBxB GBBGBxB GBBGBBB

GGxBxBx GGGBGBx GGGBGBB GGGBGBB

xGBxBxx xGBxBxx xGBxBxx GGBBBGG

xBxGxGx xBGGGGx BBGGGGB BBGGGGB

BxBxxxx BxBxBxx BxBBBxx BGBBBGG

Stacey, Rhonda, and Teresa occupy positions that sum to a prime number (clue 1). The only sets of three positions that sum to a prime number are:

8, 9, 12 (sum 29)

9, 10, 12 (sum 31)

Per clue 1, Stacey does not border either Rhonda or Teresa. With either set, Stacey is at position 12.

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