### Brain Teasers

# Class Photo

Jacob's class picture has 40 photos arranged in a 8 x 5 grid. The photos in the top row are numbered 1 through 8 from left to right, with the photos in the remaining rows similarly numbered (as shown below). Given the following clues (bordering includes horizontal, vertical, and diagonal), where is Jacob's picture?

X X X X X X X X (1 - 8)

X X X X X X X X (9 - 16)

X X X X X X X X (17 - 24)

X X X X X X X X (25 - 32)

X X X X X X X X (33 - 40)

1) There are 20 boys and 20 girls.

2) Each row and column has at least two girls, but no more than four girls.

3) Every girl borders at least one other girl.

4) Girls are located at positions that are prime numbers.

5) Boys are located at positions that are either squares or cubes.

6) Jacob is the only boy that borders a unique number of girls.

X X X X X X X X (1 - 8)

X X X X X X X X (9 - 16)

X X X X X X X X (17 - 24)

X X X X X X X X (25 - 32)

X X X X X X X X (33 - 40)

1) There are 20 boys and 20 girls.

2) Each row and column has at least two girls, but no more than four girls.

3) Every girl borders at least one other girl.

4) Girls are located at positions that are prime numbers.

5) Boys are located at positions that are either squares or cubes.

6) Jacob is the only boy that borders a unique number of girls.

### Hint

The number 1 is not a prime number.### Answer

Per clue 4: girls are at positions 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, and 37. Per clue 5: boys are at positions 1, 4, 9, 16, 25, 36, 8, and 27.B G G B G _ G B

B _ G _ G _ _ B

G _ G _ _ _ G _

B _ B _ G _ G _

_ _ _ B G _ _ _

Per clue 2: make sure each row/column has at least two, but no more than four, girls. This puts boys at positions 6 and 21, and a girl at position 33.

B G G B G B G B

B _ G _ G _ _ B

G _ G _ B _ G _

B _ B _ G _ G _

G _ _ B G _ _ _

There are still seven girls to identify, which must be assigned to columns 2, 4, 6, and 8 (clues 1 and 2). This means that boys must fill the open spaces in the other columns (positions 15, 35, and 39).

B G G B G B G B

B _ G _ G _ B B

G _ G _ B _ G _

B _ B _ G _ G _

G _ B B G _ B _

Since all girls must border at least one other girl (clue 3) and only one more girl can be added to column 2, the next placements can be made (girls at positions 14 and 26).

B G G B G B G B

B _ G _ G G B B

G _ G _ B _ G _

B G B _ G _ G _

G _ B B G _ B _

The rest of column 2 must be boys (positions 10, 18, and 34).

Because no row can have more than 4 girls, each row must have exactly 4 girls. Girls must then be at positions 12, 38, and 40. Boys must then be at positions 22 and 30.

B G G B G B G B

B B G G G G B B

G B G _ B B G _

B G B _ G B G _

G B B B G G B G

The final two girls must be at either positions 20/32 or 24/28 (clue 2). If the first combination is chosen, then there will be no boy that borders a unique number of girls (clue 6). By placing the girls at the second combination (and boys at the first combination), clue 6 will be satisfied.

B G G B G B G B

B B G G G G B B

G B G B B B G G

B G B G G B G B

G B B B G G B G

The boys in the first row border (1, 5, 4, 1) girls.

The boys in the second row border (2, 5, 4, 3) girls.

The boys in the third row border (4, 6, 5, 5) girls.

The boys in the fourth row border (3, 3, 5, 4) girls.

The boys in the fifth row border (2, 2, 3, 3) girls.

The only boy that borders a unique number of girls is the boy who borders six girls, which is at position 20. Therefore, Jacob is at position 20.

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## Comments

You lost ME

Aug 13, 2005

Either the answer is 8, (uniquely boardered by 1 girl) or you need one more clue, because the only way to come to any conclusion is to realize every row must have 4 girls in it to add up to 20. Which leaves you guessing repeatedly and not solving anything. Also, in the answer explaination, girls must be added to columns 2,4,6 & 8 not 2, 4, 6, & 7. 7 already had the min. 2 girls in it.

You are correct about being column 8, not 7. I am submitting the correction. However, the rest of the clues and steps are correct. The boy at position 8 borders 1 girl, but so does the boy at position 1, so that is not unique.

I liked this one, thanks! Solved it without a problem, but liked the brain exercise!

wow that was a long one!

I had it correct down to that final choice of pairs. But not having worked the problem in the same order shown in your solution, the fact that the solution hinged on the 20/32 and 24/28 choice was not apparent. Having considered that you might have made a mistake and there was no unique number of girls, I did not attempt to rearrange the seating to create a unique situation. It was a good teaser. I was just lazy.

Sep 12, 2005

I'm a little confused! Isn't (1) a prime number?

another minesweeper version! i love every step of it's elimination reasoning...one of my easy breezy 2 mins teasers...

39 na!

39 na!

Mar 28, 2006

Actually, there seems to be another solution to this question.

B G G B G B G B

B B G G G G B B

G B G B B(B)G G

B G B B G G G B

G B B G G B B G

And with Jacob sitting at position 22 in this matrix, you still would have him as the unique guy with 6 girls bordering him.

B G G B G B G B

B B G G G G B B

G B G B B(B)G G

B G B B G G G B

G B B G G B B G

And with Jacob sitting at position 22 in this matrix, you still would have him as the unique guy with 6 girls bordering him.

srik, your solution has a girl at position 36, which, by clue 5, must be a boy.

Boy did I blow that one. Had to go back and re-work it because I read the "squares or cubes" question as literally. I was trying to put the boys in the grid in squares! For example, 1, 4, 25, 28 made a nice square! Since the first row already had 4 girls, I filled in the remaining top spots with boys and then tried to make squares of the boys in the grid. Felt silly after reading the answer.

Great teaser the second time through!

Great teaser the second time through!

I didn't get it, but that's nothing new. I'm not good at Logic Problems, have finished very few. But I keep trying! LOL

Thanks! ~Z

Thanks! ~Z

I don't get that solution.

The girl at 26 does NOT border any other girl! Am I the only one to see this or am I utterly confused:

The only solution in my opinion is position 16 bordering 0 Girls.

There are 2 grids, both have him at 16 though. Here it is:

BGGBGBGB

BBGGGGBB

GBGBBGGB

BBBGGBGG

GGBBGBBG

If somone tells me that this is correct I might show you how to get it

The girl at 26 does NOT border any other girl! Am I the only one to see this or am I utterly confused:

The only solution in my opinion is position 16 bordering 0 Girls.

There are 2 grids, both have him at 16 though. Here it is:

BGGBGBGB

BBGGGGBB

GBGBBGGB

BBBGGBGG

GGBBGBBG

If somone tells me that this is correct I might show you how to get it

I see now my mistake, bordering also is valid **diagonally**, additionally one of my girls does not border any other

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