Download Math-a-thon Puzzles Rules and Examples NUMBER GRIDS

Math-a-thon Puzzles
Rules and Examples
NUMBER GRIDS
NUMBER PLACEMENT
Fill in the missing numbers, so that all of the numbers (1-3 for a 3x3 grid, 1-4 for a
4x4 grid, etc.) appear only ONCE in each row (across) and ONCE in each column
(vertical).
Incorrect
2 appears twice in
this row
Correct
1
2
3
2
3
1
3
1
2
1
1 appears
twice in this
column
2
2
2
1
CAGES AND CLUES
The heavy lines indicate areas (called CAGES) that contain groups of numbers that
can be combined (in any order) using the operation shown to make the answer
that appears in the cage.
4+
1-
18+
These two boxes are in a CAGE together.
The 1- means that these two numbers can be used,
IN ANY ORDER, to create a subtraction problem
with an answer of 1.
A number may appear more than one time within a single CAGE, as long as
the number is does not appear more than once in the same row or column.
**Note that we will use a slash (/) to indicate division instead of the traditional
symbol (÷) to avoid confusion with the plus sign (+).
SAMPLE SOLUTION:
The puzzle we are looking at is a 3x3 grid.
The numbers 1, 2 and 3 will be used to solve this puzzle.
4+
1-
1-
8+
These 3 boxes are in a CAGE.
The rule of this cage is 8+ which means that the
numbers in these boxes can be used to create an
ADDITION problem with an answer of 8.
The only way to get a sum of 8, using the numbers 1,2 and 3, is:
2+3+3=8
So this cage must contain the numbers 2, 3 and 3.
Here are some ways to place these numbers in the cage:
4+
1-
18+
3
3
4+
1-
2
These two options are
INCORRECT because the 3
appears twice in the same
row or in the same column.
Same
column
Same row
4+
1-
18+
2
3
3
3
1-
This solution is CORRECT because even though the 3s
are in the same CAGE, they are not in the same
column or row.
8+
3
2
3
AND 3+2+3= 8 fits the rule of this CAGE (8+).
There are several ways to continue solving this
puzzle, but the simplest is to remember the rule
that each number must appear once and only
once in each column and row.
This column already has two numbers in it. What
is the missing number?
4+
1-
18+
3
2
3
1 is the missing number so it must go in the
empty box of this column.
4+
1-
1
1-
The 1 is in a CAGE with one other number.
8+
3
2
3
The rule of the cage is 4+.
Which means that 1 and another number
must be able to make an addition problem
with an answer of 4.
1+?=4
4+
3
1-
1-
1
1+ 3 = 4, so the empty box must have
a 3 in it.
8+
3
2
3
4+
3
1-
Now, using the rule that every number must
appear once and only once in every row and
every column, we can figure out what number
is missing from the top row.
3
The row has 1 and 3.
2 is missing from this row.
1
1-
8+
3
2
4+
Now that we have placed the 2, we can look at
two things:
1-
3
1
1-
2
First, we can look at the column and see that
only one number is missing. The missing
number is 1.
8+
3
3
2
Second, we can look at the CAGE that 2 is in.
The CAGE has a rule of 1-. Which means that
we can create a subtraction problem with an
answer of 1 using 2 and another number IN
ANY ORDER.
?-2=1
3-2=1
or
or
2-?=1
2-1=1
There is already a 3 in this row so the first
subtraction problem cannot work.
Either way you solve it, the missing number in
this column is 1.
4+
3
1-
1-
1
8+
2
2
3
1
1
2
3
The numbers in the last two empty
squares can be found by looking at the
row and determining which of the
three numbers is missing from that
row. The clue in the CAGE can be used
to check your answer.
Hints:
When things look tricky, BE TRICKY!!
Look for the places where a number CANNOT BE.
1-
5+
1
This puzzle has two 1s already in it. Let’s see if we
can figure out where the last 1 goes….
4+
2
3
1
Remember 1 can only appear once in any row or
column.
6+
3
1-
These columns already have a 1 in them. So the
missing 1 cannot be in either or these columns.
5+
1
4+
2
3
1
The dashed lines represent squares that the
number 1 CANNOT be in.
6+
3
1-
5+
These rows already have a 1 in them. So the
missing 1 cannot be in either or these columns.
1
4+
2
3
1
6+
The dashed lines represent squares that the
number 1 CANNOT be in.
3
1-
5+
1
There is only one square left that 1 can be in!!
4+
2
3
1
Now that is some tricky thinking!!
6+
3