# Tutor Hunt Questions

“1. On which date was the hundredth day of the year 2008?

2. Using 4 straight cuts, what is the maximum number of pieces that a circular apple pie can be cut into?

3. Three days ago, yesterday was the day before Sunday. What day will it be tomorrow?

2. Using 4 straight cuts, what is the maximum number of pieces that a circular apple pie can be cut into?

3. Three days ago, yesterday was the day before Sunday. What day will it be tomorrow?

7 years ago

Maths Question asked by Zak

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## 11 Answers

#### Accepted Answer

1) 9th April.

2) The answer is 11.

3) Thursday

2) The answer is 11.

3) Thursday

1. 9th of April, no leap year. 31 days Jan + 29 days Feb + 31 days Mar is 91 days leaves 9 left for April.

2. 8 pieces

3. Thursday. Three days ago yesterday is four days ago, which is a Saturday. So the starting day must be a Wednesday, meaning tomorrow is Thursday.

2. 8 pieces

3. Thursday. Three days ago yesterday is four days ago, which is a Saturday. So the starting day must be a Wednesday, meaning tomorrow is Thursday.

1. 2008 is a leap year. So, there would be 31 days in January, 29 days in February, 31 days in March, which adds up to 31+29+31=91, so the next 9th day of April would be the 100th day of the year 2008

2. We would get the maximum number of slices if we can cut the maximum number of intersections with the previous lines. It would be 11 slices.

3. Three days ago, yesterday was day before Sunday i.e. Saturday. So, the day we are talking about is Sunday. Three days after that is wednesday and tomorrow would be Thursday.

2. We would get the maximum number of slices if we can cut the maximum number of intersections with the previous lines. It would be 11 slices.

3. Three days ago, yesterday was day before Sunday i.e. Saturday. So, the day we are talking about is Sunday. Three days after that is wednesday and tomorrow would be Thursday.

1 Determine if February is a leap year and the answer is yes, it is.

Jan + Feb + Mar

31 + 29 + 31= 91

so 100th day is 9th of April 2008

2. Every cut leads to its multiple in 2s in pieces, sizes could be anything

1 cut is 2 pieces

so, 4 cuts x 2= 8 pieces

3. The day before Sunday is Saturday. three days before Sat were Sunday Monday and Tuesday. so in this context, Today is a Wednesday and tomorrow will be Thursday.

I hope they answer your questions.

Jan + Feb + Mar

31 + 29 + 31= 91

so 100th day is 9th of April 2008

2. Every cut leads to its multiple in 2s in pieces, sizes could be anything

1 cut is 2 pieces

so, 4 cuts x 2= 8 pieces

3. The day before Sunday is Saturday. three days before Sat were Sunday Monday and Tuesday. so in this context, Today is a Wednesday and tomorrow will be Thursday.

I hope they answer your questions.

1) 2008 is a leap year so February has 29 days. 31 for January plus 29 for February = 60. 31 for March = 91. So the date was the 9th April.

2) to maximise each slice should have the maximum number of intersections with the previous slices. The answer is 11.

3) Thursday

2) to maximise each slice should have the maximum number of intersections with the previous slices. The answer is 11.

3) Thursday

(Q1) We start by taking off 31 days to cover Jan leaving us with 100-31=69 days.

Next we have to be a little careful as the number of days in Feb is either 28 or 29 depending on whether or not it lies in a leap year. A leap year occurs if the year is exactly divisible by 4 but not divisible by 100. If it is divisible by 100 then it is still a leap year if it is also divisible by 400. Using these rules we can see that 2008 was indeed a leap year.

We therefore need to take off another 29 days to cover the whole of Feb leaving us with 69-29=40 days.

Next is March which has 31. So we can take off another 31 days to cover the whole of March leaving us with 40-31=9 days.

We are now in April and have 9 days left which means the 100th day of 2008 must have been 9th April.

(Q2) The answer to this can vary depending on the restrictions. e.g. are you allowed to cut the apple pie horizontally? are you allowed to move the pieces after each cut? do the cuts have to be from one end of the pie to the other end?

(Q3) Work backwards here. "the day before Sunday" is Saturday, leaving "3 days ago, yesterday was Saturday". "yesterday was Saturday" becomes "Sunday", leaving "3 days ago, it was Sunday". You should be able to solve this.

Next we have to be a little careful as the number of days in Feb is either 28 or 29 depending on whether or not it lies in a leap year. A leap year occurs if the year is exactly divisible by 4 but not divisible by 100. If it is divisible by 100 then it is still a leap year if it is also divisible by 400. Using these rules we can see that 2008 was indeed a leap year.

We therefore need to take off another 29 days to cover the whole of Feb leaving us with 69-29=40 days.

Next is March which has 31. So we can take off another 31 days to cover the whole of March leaving us with 40-31=9 days.

We are now in April and have 9 days left which means the 100th day of 2008 must have been 9th April.

(Q2) The answer to this can vary depending on the restrictions. e.g. are you allowed to cut the apple pie horizontally? are you allowed to move the pieces after each cut? do the cuts have to be from one end of the pie to the other end?

(Q3) Work backwards here. "the day before Sunday" is Saturday, leaving "3 days ago, yesterday was Saturday". "yesterday was Saturday" becomes "Sunday", leaving "3 days ago, it was Sunday". You should be able to solve this.

1) Wednesday 9th April (2008 was a leap year and so 29 days in Feb)

2) I`m not sure about the maths behind this, but I can make 11:

I) One cut through the middle,

II)One perpendicular to this cut (you should now have 4 pieces)

III) One diagonally through both these but NOT through the centre (ie you should cut each line at different points, now having 7 pieces)

IV) Forth cut should intersect three lines, but again not at any point at which two other lines intersect. (You now have 11)

3)Work backwards from Sunday:

The day before Sunday was Saturday.

Count Three days ahead - Sunday, Monday, Tuesday.

This was yesterday, so today is Wednesday.

Tomorrow is therefore Thursday.

2) I`m not sure about the maths behind this, but I can make 11:

I) One cut through the middle,

II)One perpendicular to this cut (you should now have 4 pieces)

III) One diagonally through both these but NOT through the centre (ie you should cut each line at different points, now having 7 pieces)

IV) Forth cut should intersect three lines, but again not at any point at which two other lines intersect. (You now have 11)

3)Work backwards from Sunday:

The day before Sunday was Saturday.

Count Three days ahead - Sunday, Monday, Tuesday.

This was yesterday, so today is Wednesday.

Tomorrow is therefore Thursday.