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CHALLENGE 56

Given 2 pairs of numbers 1) what is the missing number to make a thrid pair. 2) What is the relationship between pairs:
Answer in Comments Section below:
Quiz by Malbaby
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Last updated: October 31, 2020
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First submittedOctober 31, 2020
Times taken1
Average score100.0%
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Number Pairs:
 
21 / 36
answer
36 / 64
in
? / 441
comments
7 Comments
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mushroomsteve
+1
Level 53
Nov 1, 2020
I don't think this is right, but is the missing number 231?
Malbaby
+1
Level 71
Nov 1, 2020
Yes 'mushroomsteve' you have done it again. I thought I would slip in another number challenge incorporating one of my favourites. Another Honorary Gold Medal on it's way.
Malbaby
+2
Level 71
Nov 1, 2020
As you suggest 231 is the cumulative number of 21 and 441 is the square of 21. As with 6 c no. 21 square 36 and 8 .. c.no. 36 square 64........... I have fun with these numbers, such as the sum of the c.nos. of two adjacent numbers (e.g. 9 / 10) equals the square of the highest (100) and the difference between a c.no. and its square is equal to the c.no. of the number before. e.g. 5 c.no = 15 square 25 difference 10 which equals the c.no. of 4.
mushroomsteve
+1
Level 53
Nov 1, 2020
Yes, they are quite fun! The nth one is given by T(n) = n(n+1)/2, so as you say we get T(n) + T(n-1) = n(n+1)/2 + n(n-1)/2 = n^2. I remember one time trying to find on a tiny scrap of paper all of the triangular numbers that are exactly double another triangular number. They are really fun to play around with.
PotatoBoy
+1
Level 66
Nov 2, 2020
As I was about to tie with steve in number of medals, just like that he nails 2 challenges in a row....
ylj
+1
Level 54
Nov 2, 2020
^_^
Malbaby
+1
Level 71
Nov 2, 2020
Top 5 medal winners so far: 'mushroomsteve' with 10, then 'PotatoBoy' with 8, followed by 'ylj' and 'overtired' with 7 and they are followed by 'colmaggio' and 'Kiwirage' with 6 each. Congratulations medal winners.
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