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Count Rectangles, Find the States and Adding Puzzle

Here are some puzzles based on Pierre Berloquin's book '365 Exercises for the Mind'. The solutions to these puzzles can be found at the bottom of the page. Try to resist peeking until you have given yourself time to try to solve the puzzles.

Number Patterns Math Puzzle

Take a long look at the numbers below. See if you can find the pattern or logical relationship among the blue numbers. Which red number should actually belong to the group of blue numbers?

234 678
111213 14910
8716 151413
432 1279
121315 468
132 181112



Adding Numbers Puzzle

The following puzzle is not all that challenging but fun nonetheless. Select as many numbers as necessary to make the total add up to 30. The numbers must be adjacent either across are down but not diagonally. There is more than one solution to this puzzle.


Counting the Rectangles Geometric Puzzle

Study the geometric picture below. If you were to remove the diagonal lines, how many squares and rectangles can you see?

Rectangle Geometric Puzzle



Find the States Word Puzzle

See if you can come up with 14 U.S. states that begin with at least two of the letters below.

M - A - I - N - E



Solutions

Resist the urge to peek until you have exhausted all possibilities

Number Patterns Math Puzzle

Most of us did not see any pattern of all. However, one clever staff member picked up the correct solution almost immediately. The simple solution is the fact that the blue numbers are all multiples of three. The red number 12 that is four rows down and four columns across is also a multiples of three and should actually be blue. It is amazing that something so simple can be so hard to find.

Adding Numbers Puzzle

There is more than once solution to this puzzle. One of the solutions follows.

7 + 2 + 4 + 5 + 1 + 8 + 3 = 30.

Counting the Rectangles Geometric Puzzle

You need to look real hard here. There are many rectangles that are not obvious. In fact, none of our staff guessed correctly, but a few came close. There are nine rectangles that were actually drawn to make this geometric design. The overlaps are easy to find, but the gaps are often missed. Another area that tricked us was the fact that two rectangles often made a larger rectangle. The diagonals most likely distract the flow of the eye as well. Believe it or not, there are 31 rectangles in the picture.

Find the States Word Puzzle

The 14 states are Indiana, Maine, Maryland, Massachusetts, Michigan, Minnesota, Mississippi, Missouri, Nebraska, Nevada, New Hampshire, New Jersey, New Mexico, and New York.
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