No 49

Repfigits

 

197 is an amazing number. It has three digits. If you take the "digit sum" 1+9+7=17 and then continue adding in threes in "fibonacci style" look what happens:

1 + 9 + 7 = 17

9 + 7 + 17 = 33

7 + 17 + 33 = 57

17 + 33 + 57 = 107

33 + 57 + 107 = 197

We arrived back at 197! The number 197 is called a REPFIGIT. Here is another example:

75 has two digits. So this time you take the addition in twos as follows...

7 + 5 = 12

5 + 12 = 17

12 + 17 = 29

17 + 29 = 46

29 + 46 = 75

... arriving back at 75.

There are only six two digit numbers that are Repfigits, 75 is one of them. Can you find the other five. Amazingly 197 is one of the only two 3 digit Repfigits. Can you find the other one? And then of course there are the nine 4 digit Repfigits and the seven 5 digit Repfigits and.... and...

If you have answers, discoveries, new questions etc to do with this Number Fact then...

E-mail us at madrascollege.maths@fife.gov.uk

...and we will publish them here.

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