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Tips on Solving Logic Problems - a logic problem

THE PUZZLE:

Five sisters all have their birthday in a different month and each on a different day of the week. Using the clues below, determine the month and day of the week each sister's birthday falls.

  1. Paula was born in March but not on Saturday. Abigail's birthday was not on Friday or Wednesday.
  2. The girl whose birthday is on Monday was born earlier in the year than Brenda and Mary.
  3. Tara wasn't born in February and her birthday was on the weekend.
  4. Mary was not born in December nor was her birthday on a weekday. The girl whose birthday was in June was born on Sunday.
  5. Tara was born before Brenda, whose birthday wasn't on Friday. Mary wasn't born in July.

HOW TO SOLVE IT:

The grids provided to help solve logic problems are useful for identifying what you have learned from each clue. Where the vertical and horizontal squares meet are your possible answers and these will be crossed out as each is proven to be false. When you find a true match, draw a black dot in the appropriate square. When you prove a combination false, draw an 'x' in the square.

Clue 1: The first clue states that Paula was born in March so put a black dot in the square for "Paula" and "March" as shown. Since Paula was born in March, none of the other possibilities are valid, so the rest of the row and column can be marked with an 'x' as shown. The clue also states that Paula's birthday is not on Saturday, thus "Saturday" for "Paula" can also be crossed out as shown. The second half of the clue states that Abigail's birthday is not on Wednesday or Friday so you can mark Wednesday and Friday for Abigail with an 'x' in the right section of the grid as shown.

Clue 2: According to the second clue, Brenda and Mary could not have been born in February since the girl whose birthday is Monday was born earlier in the year. Likewise, Brenda and Mary didn't have a birthday on Monday. So these squares can be crossed out. Also, in the bottom part of the grid, the Monday birthday cannot happen in July or December because both Brenda and Mary had birthdays AFTER the girl whose birthday is on Monday so these two squares can also be crossed out as shown.

Clue 3: Tara was not born in February and so that square is crossed out. Now the only square in that row that isn't crossed out is Abigail. By elimination therefore, Abigail was born in February. Put a black dot in that square and cross out the rest of the horizontal row. In addition, since you know from clue 1 that Abigail's birthday is not on a Friday or a Wednesday and you know she was born in February, you can cross out Wednesday and Friday in the bottom block of the grid for February. Also, from the second half of Clue 3, Tara's birthday is on the weekend, so Monday, Wednesday, and Friday are crossed out for Tara in the right section of the grid as shown.

Clue 4: Mary wasn't born in December so cross it out as shown. Since her birthday isn't on a weekday, you can also cross out Wednesday and Friday for Mary in the right-hand section of the grid. From Clue 2 you know that Tara's birthday was on a weekend too. So in the right section of the grid, Saturday and Sunday can be crossed out for Abigail, Brenda, and Paula. This leaves only Monday for Abigail to put a black dot in this square and cross out the rest of the column for Monday. From the last part of Clue 4, in the bottom section of the grid, put a dot for June and Sunday, crossing out the rest of the column and row respectively as shown. Also, in the upper grid, cross out Brenda for June because you know her birthday wasn't on the weekend.

Clue 5: Since Tara was born before Brenda, cross out December for Tara since she couldn't have been born last. This leaves only December for Brenda so put a black dot in that square and cross out the rest of the row. From the second half of the clue, you know that mary wasn't born in July so by elimination Tara was born in July. Put a black dot in that square and cross out the rest of the row. Also put a black dot in the square for Mary and June since it's the last square open. You've now determined all of the months in which everyone was born. Also, since you know that June goes with Sunday and Mary was born in June, her birthday is on Sunday so mark that off in the right section of the grid. This then leaves Tara for Saturday so mark that too. Lastly, from the clue, Brenda's birthday wasn't on Friday. So by elimination, Brenda's birthday was on Wednesday and Paula's birthday was on Friday.

CONGRATULATIONS!
You've now completed the logic problem. You should have a full grid that looks like the one below. Or in summary, you should have the following answer:

FINAL SOLUTION:

  • Abigail, February, Monday
  • Brenda, December, Wednesday
  • Mary, June, Sunday
  • Paula, March, Friday
  • Tara, July, Saturday


 
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