Matrix logic or logic grid puzzles challenge you to figure out the characteristics of several people, using a series of clues, marking “yes” answers with an O and “no” answers with an X in a grid of boxes. You can see an example grid in this Wikipedia article.
My 12-year-old Nicholas enjoys matrix logic almost as much as I do, so when he asked me last night to make up a matrix logic puzzle for him, I jumped at the chance. He wanted it to have 5 people and 5 facts about each. I challenged myself to do it with just 5 clues.
This puzzle is about 5 people who have a new baby in their family. What is each person’s first name, last name, month of birth, day of birth, and relationship to the baby?
Get your graph paper! Leave about 6 blank columns at the left for labeling. Then label 5 vertical columns for the Last Name: Esposito, Favors, Ikezawa, Leapman, Santini. Draw a heavy vertical line to the right of Santini.
Next, make vertical columns for the Birth Month: March, May, July, September, October; Day of Birth: 3rd, 5th, 8th, 11th, 28th; and Relationship to Baby: great-grandmother, grandfather, father, uncle, cousin. Draw heavy vertical lines to separate the sections. Draw a heavy horizontal line under the labels.
Now, at the left, label the first 5 rows below the column labels. These rows are for First Name: Chloe, Eric, Paul, Rose, Steve. Draw a heavy horizontal line under Steve, all the way to the end of the last column (cousin).
The other horizontal sections only need to extend under enough vertical categories to create one box for every possible combination. To do this most efficiently, put Relationship to Baby under First Name and extend those rows across the columns for Last Name, Birth Month, and Day of Birth. Then put Day of Birth under Relationship and extend its rows across the columns for Last Name and Birth Month. Put Birth Month at the bottom, and its rows only need to intersect the columns of Last Name.
When you are certain of a match, mark an O in that box, and then mark X for all of that person’s other options in the section. For example, if you decide Chloe’s last name is Esposito, mark O at the intersection of Chloe and Esposito, then mark X in Chloe’s row for the other last names and X in Esposito’s column for the other first names.
When you don’t know what matches, but you know that one choice is not right, mark an X in that box. For example, Eric is a male name, so Eric is not the great-grandmother.
Got your matrix ready? Here are the clues!
- Two people have a first name that starts with the same letter as their last name.
- Uncle Steve was born in the spring.
- Chloe’s birthday always comes on the day after a national holiday. Her two uncles have birthdays that sometimes come on Memorial Day or Labor Day.
- Great-grandma Ikezawa’s day of birth is the sum of her son’s and one grandson’s days of birth.
- Mr. Favors’s birth month begins with the same four letters as the name of an animal whose number of legs equals Grandpa’s day of birth.
Nicholas solved the puzzle mostly by himself, but he needed help understanding the rules of holiday timing and needed a reminder about cross-referencing. Why don’t you see how far you can get without hints? Then, read the hints below if you need them.
Okay, now if you can’t figure out which combinations of birth month and day–from those still available–might fall on Memorial Day or Labor Day, you may look up those holidays.
Still have some boxes unfilled? Look at each place you have an O marking the match between the fact in a column and the fact in a row. Look all along that row for the other information you know about that person, and make sure all of that information is recorded in the column, and vice versa. Do this for every O. If you’re still missing something, read through all the clues again.