Challenge 4 - Last Wednesday
Challenge 4 is all about dates and square numbers.
Maths teacher Chris Smith and pupils from Grange Academy are here to explain.
The Maths Week Scotland Daily Challenges have been set by the Scottish Mathematical Council.
Mr Smith: This problem is all about dates and square numbers.
The date of the second Thursday of a particular month is a square number.
Using this information, can you work out the date of the last Wednesday of that month, assuming the month is not February?
Explain your answer.
Pupil: If you are unsure where to start, try drawing out a calendar month.
Pupil: This could then help you discover more missing information.
Pupil: You will then need to know the square numbers, try writing them all out.
Pupil: Good luck.
So here's the challenge:
This problem is all about dates and square numbers.
The date of the second Thursday of a particular month is a square number.
What is the date of the last Wednesday of that month, assuming the month is not February?
Need a hint?
If you are unsure where to start, try drawing out a calendar month.
This could then help you discover more missing information.
You need to know which numbers are square numbers, try writing them all out.
Solution
Worked out the answer? Here's how you can do it.
Did you work out the date of the last Wednesday of the month?
Let’s look at how we got our answer.
We can write out all the square numbers that could be dates: 1, 4, 9, 16, 25 …
The next square number is 36, which is too big to be a date.
The second Thursday can't be 1 or 4, as these dates could only be the first Thursday of the month.
And it can't be 25, as that could only be the fourth Thursday of the month.
The second Thursday of the month must occur between the 8th and 14th, so the only square number it can be is 9.
If the 9th is a Thursday we can work out the dates of the other Thursdays in the month. The 2nd, 9th, 16th, 23rd, 30th are Thursdays.
The last Wednesday is the day before the 30th, the 29th.
Great job if you crossed this one off.
Step 1
We can write out all the square numbers that could be dates: 1, 4, 9, 16, 25 …
The next square number is 36, which is too big to be a date.
Step 2
The second Thursday can't be 1 or 4, as these dates could only be the first Thursday of the month.
And it can't be 25, as that could only be the fourth Thursday of the month.
Step 3
The second Thursday of the month must occur between the 8th and 14th.
The only square number this can be is 9.
Step 4
If the 9th is a Thursday, we can work out the dates of the other Thursdays in the month.
The 2nd, 9th, 16th, 23rd, 30th are Thursdays.
The last Wednesday is the day before the 30th, the 29th.
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