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Mr Ashcroft's problem page

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colin ashcroft

on 16 September 2015

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Transcript of Mr Ashcroft's problem page

1.First of all, pick the number of times a week that you eat chocolate. This number must be more than one but less than ten.
2.Multiply this number by 2 (just to be bold).
3.Add 5 (for Sunday).
4.Multiply it by 50.
5.Add 1750.
6.Add the last two digits from the year you last had a birthday. So if your last birthday was in 2009, add 9, if the your last birthday was in 2011 then add 11.
7.Now subtract the four digit year that you were born (if you remember).

You should now have a three digit number. The first digit will be your original number (i.e. how many times you eat chocolate each week). The next two digits give your age. Can you explain why it works?

week 3
week 2
Can you solve this week's brain teaser!
Mr Ashcroft's problem page
week 1
Take the 2-digit number 45.
Square it (45 x 45) to make 2025
Split this 4-digit number in half to make 20 and 25
Add them (20 + 25) to make 45
Which is what you started with.
Find another 2-digit number which does the same.

A group of four people, when asked the time gave these different answers –

Jan said said it was "3 minutes past10" 
Kit said said it was "3 minutes to10" 
Nicky said said it was "6 minutes to10" 
Terri said said it was "2 minutes past10" 
They were all supposed to be telling the same time!

They were all wrong.
Their errors (in no particular order) were 2, 3, 4 and 5 minutes.

What was the correct time?

The drawing of the flag of St. George.
It consists of a red cross on a white background.
Both arms of the red cross are the same width.
The flag measures 60 cm by 91 cm.
The area of the red cross is equal to the area of white.
What is the width of the red arms?

week 4
The background represents a small sheet of 12 postage stamps, as they are usually sold, all perforated at the edges and all of the same value. (The letters are only there to identify the separate stamps).
You need 4 of the stamps in order to post a letter but would like all 4 to be properly joined together at their edges (not at their corners). For example: ABCD, EFGH, JKLM, FGHL would all do, but not EFLM.
In how many different ways can you get such a group of 4?

week 5
A group of people were gathered together in one room and it was possible to count them using the following descriptions -
1 grandmother 1 brother
1 grandfather 2 sisters
2 fathers 2 sons
2 mothers 2 daughters
4 children 1 father-in-law
3 grandchildren 1 mother-in-law
1 daughter-in-law
giving a total of 23 people. But there was far less than that.

week 6
week 7
Use the digits 0,1,2,3,4,5,6,7,8,9 use each only once.
Divide them into two groups of five, and then arrange the dogits in each group of five to make a multiplcation sum.

It could be done like this
0,1,5,6,9 used to make 106 x 59 (which is 6254)
2,3,4,7,8 used to make 437 x 82 (which is 35834)
and the two multiplication sums have different answers.
Find a way that makes the answers to both multiplication sums the same.
I recently found just the things I wanted at a car boot sale. The way they were priced was interesting,
5 for 10p
12 for 18p
14 for 20p
19 for 24p
I eventually worked out the 'logic' of the prices.
What did 11 cost me?

Kim wishes to measure out 4 litres of water,
but has only two jugs which, when full, hold
3 litres and 5 litres respectively and have no
other markings on them.
Plenty of water is available from a tap.

How can Kim measure out exactly 4 litres?
My sailing ship has two sails in the shape of right angled triangles.
They are of different areas, but each area is a whole number.
All their edge lengths are different lengths too, but are whole numbers.
However, they do have one common property, the area of each sail is the same as their perimeter.
What is the area of each sail?
I'm curious? Does this sound reasonable...
Today I ate a 30g packet of crisps at morning break time, as I always do, so I estimate that I eat almost 11kg of crisps a year.

A packet of sugar weighs 1kg. My friend and I take two spoons of sugar in our coffee and we each drink 4 cups per day. One packet should just about last us for the two month field trip that we are planning.

My round trip to work each day is about 22 miles, but I can claim mileage from work. I estimate that I can claim for 8000 miles each year.
Week 10
16 0 24
0 39 0
23 0 17
The drawing above is of a "puzzle dartboard".
Each dart scores the number written in the cell in which it lands.
You may throw as many darts as you like,
but must score exactly 100.
What is the least number of darts you would need,
and in which cells must they land?
week 11
At a recent athletics meeting, five old acquaintances: Fred, Greta, Hans, Iolo and Jan met together for
the first time since leaving college, so they had a lot of news to catch up on.
It seemed they all lived in different towns: Acton, Buswick, Coalford, Derby and Eccles; and that they all had different jobs which were, in no particular order: an engineer, a lawyer, a teacher, a doctor and a shopkeeper.
To round it off, each one was the winner in just one event at the meeting. These were: 100 metres, 400 metres, 1500 metres, High Jump and Javelin.
The following facts were also known:
1. Hans the shopkeeper from Derby won the High Jump.
2. The lawyer was from Eccles and said he was not a runner.
3. Greta was a P.E. teacher from Buswick and won the 1500 metres
4. The doctor, who came from Acton, did not win the 100 metres.
5. The person from Derby was not an engineer.
6. Iolo was an engineer from Coalford and did not win the 400 metres.
7. Jan was not a lawyer, but did win the 400 metres.
8. Fred did not come from Acton and was not a runner.
a) Which event did the person from Coalford win?
(b) Which town did Jan come from?
(c) What was the name of the lawyer?
(d) Which event did the engineer win?
(e) Which event did Fred win?

week 12
When walking at my normal pace, an exact number of (equal) paces measures out a length of precisely 14.11 metres.
How many paces does it take to do that?
week 13
week 13

Which number is two numbers to the left
of the number which is two numbers to the right
of the number which is three numbers to the right
of the number which is two to the left of the number immediately to the right of the number 4
week 14
At what time between 1pm and 2pm
do the minute hand and the hour hand
of a clock coincide exactly?

week 15
week 16
Can you find five pieces of furniture in this
grid? Choose a letter to start at and move one place up, down, left, right or diagonally to find the next.
Each letter must only be used once, and all 25 letters must be used.

The two main scales used for measuring temperature are the Fahrenheit and the Celsius scales.
Some commonly-used temperatures are shown on the right as they would be shown on those scales.
Notice that they seem to get closer together as they go down.

At what temperature do both scales read the same?
Fahrenheit Celsius
Boiling point of water 212°F 100°C
Blood heat 98.6°F 37°C
Freezing point 32°F 0°C
of water

week 17
week 18
In this building there are eight inmates, one in each cell.
How can they be arranged so there are are
four inmates along each side?
week 18
Arrange the numbers 1 to 9 in the cells
of this square so that the horizontals,
verticals and diagonals all add up to
the same number.
week 19
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