# Calendar Problems

## Problems for month and day 00/00 dates

### 1. What is pi day?

Work space:

*Hints*:

- Use 0/00 format
- Pi = 3.14159265

*Enjoy!*

### 2. What dates (month/day) are *prime* dates?

*prime*

Work space:

*Hints*:

- One isn't a prime or composite.
- Take one date at a time starting with January 1 (1/1) and check each until you find a pattern to identify answers and eliminate non answers.
- 2, 3, 5, 7, & 11 are primes.
- 2/2, 2/3, 2/5 ...2/23 , & 2/29 if a leap year.
- 3/_, 5/_, 7/_, 11/_

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### 3. Which dates (month/day) are the **months** multiples of the **days**?

**months**

Work space:

*Hints*:

- A multiple is a number that can be divided by another number without a remainder.
- Take one date at a time starting with January 1 (1/1) and check each until you find a pattern to identify answers and eliminate non answers.
- There is only one in January (1/1).
- There are two in February (2/1, 2,2).
- Two in March.
- Three in April.
- Two in May. Four in June. Two in July. Four in August. Three in Spetmber, Four in October. Two in November. Six in December.

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### 4. Which dates (month/day) in a year can be written with only one digit?

Work space:

*Hints*:

- Take one date at a time starting with January 1 (1/1) and check each until you find a pattern to identify answers and eliminate non answers.
- January has two.
- February has two.
- March has one.
- April, May, June, July, & December have ...
- October & November have ...

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### 5. Which dates (month/day) are **factor** dates?

Work space:

*Hints*:

- January has the most.
- February 2/2, 2/4, 2/6, ... 2/28
- March 3/3, 3/6, 3/9, ... 3/30
- April 4/4, 4/8, ... 4/28
- May

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### 6. Which dates (month/day) are **triangular** dates?

Work space:

*Hints*:

- Triangular numbers make a pattern that form equilateral triangles. For example: each row of dots adds to the total number of dots in another equilateral triangle.
- January has 7: 1/1, 1/3, 1/6, 1/10, 1/15, 1/21, 1/28
- March has seven: 3/1,
- June has seven
- October has seven

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### 7. Which dates (month/day) are **square **dates?

Work space:

*Hints*:

- Square numbers are 1, 4, 9, 16, 25, 36 ...
- January has five.
- April has five.
- September has five.

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### 8. Which dates (month/day) are **palindrome **dates?

Work space:

January

February

March

April

May

June

July

August

September

October

November

December

*Hints*:

- Dates can be written numerically with: two digits - 1/1, three digits - 1/11, four digits - 11/11, six digits - 11/11/11, & eight digits - 11/11/1111
- Palindromes are numbers that have the same value if read from left to right has right to left.
- April, .. October have two.
- January has four: 1/1, 1/11, 1/21, 1/31
- Februaryhas three: 2/2, 2/12, 2/22
- March, April, May, June, July, August, September, have three
- November, December two
- Eight digit dates - 12 in a 21
^{st}century

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### 9. Which dates (month/day) are **perfect **dates?

Work space:

*Hints*:

- A perfect number is a positive integer whose sum 0f all its factors, except itself, add to the number. For example: six is a perfect number, because its factors 1, 2, and 3 add to itself, 6. Twenty- eight is also: 1, 2, 4, 7, 14 add to 28.
- There are only two.

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### 10. Which dates (month/day) are **reciprocal **dates that use the same numbers inverted?

Work space:

*Hints*:

- Reciprocal dates are two dates whose product as fractions is one. For example: 1/2 * 2/1 are reciprocal.
- Reciprocal dates inverted are: 1/1 & 1/1, 1/2 & 2/1, 21/1 & 1/21.
- 1/2 & 4/2 are reciprocal, but do not have the same numbers.
- Take one date at a time starting with January 1 (1/1) and check each until you find a pattern to identify answers and eliminate non answers.

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### 11. Which dates (month/day) are **reciprocal dates in March**?

Work space:

*Hints*:

- Reciprocal dates are two dates whose product as fractions is one. For example: 1/2 and 2/1 are reciprocal; 1/2 is reciprocal with 2/1, 4/2, 6/3, 8/4, 10/5, 12/6
- Take one date at a time and check each until you find a pattern to identify answers and eliminate non answers.
- These dates 3/1 (9), 3/2 (6), 3/3 (11 not counting 3/3), 3/4 (3), 3/5 (2), 3/6 (6), 3/7 (1), 3/8 (1), 3/9 (4), 3/10 (1), 3/11 (1), 3/12 (3), 3/15 (2), 3/18 (2), 3/21 (1), 3/24 (1), 3/27 (1), 3/30 (1).

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### 12. Which dates (month/day) are **relatively prime **dates?

Chose a task:

- Find one relatively prime in each month.
- What month has the most relatively prime dates?
- Is there a string of relatively prime dates greater than 33?

Work space:

*Hints*:

- Relative primes have no common factors other than 1. In other words there is no value that you could divide them both by exactly (without a remainder). Four and fifteen are relatively prime: The factors of 4 are 1, 2, 4 and The factors of 15 are 1, 3, and 5. Therefore, the only common factor is 1. relatively prime date, is 4/15.
- List of factors for 1 - 50.

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### 13. Additonal** **date puzzles?

Puzzles:

- What dates are square dates?
- What dates are cube dates?
- What dates are square root dates?
- What dates are cube root dates?
- Dates that are composites or not primes.
- How many consecutive digit dates can be made with six place dates 00/00/00?

Work space:

*Hints*:

- Square dates: month number is the square of the day.Example: 3/9
- Cube dates: month number is the cube of the day.Example: 3/27
- Square root dates: month number is the square root of the day.Example: 9/3
- Cube root dates: month number is the cube root of the day.Example: 27/3
- Primes have a factor of one and itself. One is neither a prime or composite.
- Six place dates with consecutive digits: 10/11/12.

*Enjoy!*

## Problems for month, day, year 00/00/00 dates

### 1. What is pi day?

Work space:

*Hints*:

- Use 0/00/00 format
- Pi = 3.14159265

*Enjoy!*

Adapted from: *Mathematics Detectiv*e. *Mathematics Teaching in the Middle School*. Volume 4, Number 1: September 1998, p. 37-39.