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Sept 03

What is the last digit of the number 1 / 5^903 ?

Too Close to Call

Weekly Problem 24 - 2012
Can you put these very close fractions into order?

Fractional Wall

Using the picture of the fraction wall, can you find equivalent fractions?

Matching Fractions, Decimals and Percentages

Age 7 to 14 Challenge Level:

A pupil from Gamlingay Village Primary sent in the following:

At first my card choices were random, but when I had remembered some cards I tried to match them and remember what was on each card. I also tried to convert the numbers on the cards into the same thing (e.g: decimals, fraction or percentage), which made it easier to tell if they matched one I had remembered.


Madeleine from the British School of Manila in the Philippines had a similar strategy:

My strategy was to look at random ones and guess at the beginning, then at the end I would remember where pairs were and do them quickly.


Callum from Wembrook Primary School wrote:

All you have to do is memorise the cards you have already flipped over and when you find one either in a decimal, a percentage or a fraction you have already found just match it to the equivalent card.


Erik from International School of the Hague (ISH) in the Netherlands wrote:

I did the matching fractions, decimals and percentages problem. The fastest way to get all the cards matched (if you are on cards up) is focusing on the easiest ones first. After you have matched all the easy ones, you have narrowed down the hard ones' possible answers. If you start on the harder ones, you will be looking through the flash cards to find an answer, and that will take you longer and you will get a higher time. Don’t work hard, work smart.


Christopher from England wrote:

I recorded what each square was on a piece of paper as a fraction in its simplest form. Then, I matched them up, ticking them off as I went.


Mark from the International School of the Hague wrote:

First, I converted all the irregular values to decimals, to make them equal. For fractions, I converted the denominator to a hundred and then the numerator accordingly, so that the denominator was equal to hundred. The numerator was then the tenths and hundredths place of the decimal.

For the shapes, I counted how many there were in total and then how many were shaded to a fraction. The number of how many were shaded was the numerator and the total number was the denominator, I then did the same process as the fractions. And completed it.


Mahdi from Mahatma Ghani International School in India focused on finding the pairs as quickly as possible with the cards face-down, once you are already fluent with converting between the fractions, decimals and percentages. This is Mahdi's strategy:

For the face-down cards, I started to open the cards two at a time, labeled 1 and 2. If the two match, I open the 3rd and the 4th and continue. If 1 and 2 don't match (which is very likely), I proceed to open the 3rd one. I then recall whether the 3rd matches with any of the previous ones (1 and 2) in any simplified form. If not, I open the forth and continue. This was the general strategy I followed. 

Also, I found out that [by] the 9th card I will definitely have a match. This is due to the pigeon-hole principle (if the first 9 cards were all different to each other, then they would each still have a pair somewhere else - so there would be 9 partner cards - but there are only 16 cards althogether). So, in the worst-case scenario every card from 1 to 8 has a corresponding match from 9 to 16 in some order. Thus when I open the 9th card it will definitely have a match for one of the 1-8 cards. This makes the strategy easier because I only have to memorize cards till 8 if there is no match. Otherwise, the game will get a lot easier if I luckily get a match before that.