# 13 Plus 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

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

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?

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:

• 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 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.
• 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 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 ...
• 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 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:

• Palindromes are numbers that have the same value if read from left to right has right to left.
• 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.
• 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

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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.
• 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 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?

• 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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Puzzles:

1. What dates are square dates?
2. What dates are cube dates?
3. What dates are square root dates?
4. What dates are cube root dates?
5. Dates that are composites or not primes.
6. How many consecutive digit dates can be made with six place dates 00/00/00?

Work space:

Hints:

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

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## 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 Detective. Mathematics Teaching in the Middle School. Volume 4, Number 1: September 1998, p. 37-39.