Three Winter Math Puzzles

Welcome to Math Plus Blog and join us towards enhancing students' performance in mathematics. We will start our journey with some selected puzzles as one of the most natural ways to connect mathematics with logical reasoning and vice versa. First, try to solve the puzzles, and then look for their solutions at the end of the post. Estimated level: 3rd Grade Math.

Math Puzzle 1

Put the letters S, N, O, W in the table below, in such way that in each row, in each column and in each small square, each letter appears only once.

Math Puzzle 2

The Koch snowflake is formed iteratively, starting from an equilateral triangle, following the same rule for each side of the figure: replace the middle third with an equilateral triangle, then delete the base of the inserted triangle. On the picture below, the first figure, the starting triangle, has 3 sides; the second figure, the first iteration of the Koch snowflake has 12 sides; and the third figure, the second iteration of the Koch snowflake has 48 sides. How many sides does the next iteration of the Koch snowflake have?

Math Puzzle 3

In how many ways can you read the word WINTER from the chart bellow?

W
I     I
N   N   N
T    T    T    T
E    E    E    E    E
R    R    R    R    R    R

Answers

Math Puzzle 1

The letters should be placed in the following way:

Math Puzzle 2

According to the rule of forming the next figure from the previous one, each side is replaced by 4 new sides. This means that the next iteration will have 192 (= 48 · 4) sides.

Math Puzzle 3

If reading means looking only for neighboring letters to form a word, then for each letter there are two ways to go to the next letter (going left or right). This means that there are two ways to go from W to I, for each I there are two ways to go from I to N, for each N there are two ways to go from N to T, for each T there are two ways to go from T to E, and for each E there are two ways to go from E to R. So, in total, there are 2 · 2 · 2 · 2 · 2 = 32 ways to read the word WINTER. Note that in the final product there are five 2s, which is exactly how many passages are there from one letter to another in the word WINTER, six letters - five passages.

I hope you enjoyed solving these winter puzzles!