Question

How many pairs of these numbers add up to a multiple of 11.

9, 46, 79, 13
64, 90, 2, 97,
25, 31, 20, 22
4, 52, 55, 7

How could you convince someone that they haven't missed any?

Notice anything interesting about the pairs of numbers?

Can you explain what's happening?

Answer 1

Yeah @chrisabraham87

Answer 2

a + b = 0 (11)

a = -b (11) maybe

Answer 3

Any ideas?

Answer 4

A grid.

Answer 5

Can you answer the questions please?!

Answer 6

Sure just let me figure it out.

Answer 7

Thank you

Answer 8

Follow the numbers and see where they go.

Answer 9

?

Answer 10

chris, please dont expect us to answer your question for you without you providing some input and effort towards a solution.

Answer 11

That's 1 pair.
------------
Remove 22 & 55
-----
9, 46, 79, 13
64, 90, 2, 97,
25, 31, 20,
4, 52, 7
14 numbers remain. Try them 2 at a time, starting with 9.
There are 5 pairs with 9.
Eliminate the 9, try 46.
46, 79, 13
64, 90, 2, 97,
25, 31, 20,
4, 52, 7
There are 4 more pairs with 46.
Eliminate the 46, etc.
79, 13
64, 90, 2, 97,
25, 31, 20,
4, 52, 7
4 pairs with 79
-----------
13
64, 90, 2, 97,
25, 31, 20,
4, 52, 7
4 pairs with 13
--------------
64, 90, 2, 97,
25, 31, 20,
4, 52, 7
2 pairs with 64
-------------
90, 2, 97,
25, 31, 20,
4, 52, 7
3 with 90
----------
2, 97,
25, 31, 20,
4, 52, 7
3 with 2
-----------
97,
25, 31, 20,
4, 52, 7
None with 97
------------
25, 31, 20,
4, 52, 7
1 w/25
------------
31, 20,
4, 52, 7
None w/31
------
20, 4, 52, 7
None w/20
-----------
1 w/4 and that's all
28 total.

Answer 12

There are 16 numbers. 2 of them are multiples of 11, 22 & 55, so they can only be added to each other --> 77. Adding any other number to them won't work.

Answer 13

oy thats alot to read :) good job tho

Answer 14

Posts should be other way around.
Can anyone help me answering the 3 questions on the task?

Answer 15

is the block of numbers a single set? or is that 4 different sets?

Answer 16

It's a grid

Answer 17

So any combination of numbers so long as they are multiples of 11

Answer 18

is this number theory by chance?

Answer 19

I am not sure at all

Answer 20

no idea on the first question, i cant even convince some people that 1+1 =2 ....

Answer 21

the smallest pair, im assuming a pair to be the sum of 2 number, is 2+4=6
lhe largest pair is 97+90 = 187

to give a range of values between 6 and 187

Answer 22

Must be multiples of 11 mate

Answer 23

i know that multples of 11 in this range take the form:

11(a,b) = a, a+b, b

11(n) = 187 ; therefore n=17

right, nust be a multiple of 11, and since i dont know a cookie cutter response there is a systematic process to go thru to determine if a suitable solution exists

Answer 24

ive never seen the grid tho, so i cant say i know if this pertains to number theory or something else

Answer 25

11 = 10+1
11n = 10n + n

79+25 = (70+20) + (9+5)
= (70+20+10) + (4)
= 10(10) + 4 ; since 10 not equal 4, this isnt a multiple

Answer 26

alright, here's the short way to do this:
rewrite all the numbers in mod 11 (i.e. remainder when divided by 11).
you get:
9,2,2,2,9,2,2,9,3,9,9,0,4,8,7
that's five 2's, five 9's, one 3, one 8, one 4, one 7.
any of the 2's paired with any of the 9's gets u 11, counting that gives 25 pairs, then the 3-8 is one pair, the 4-7 is one pair, for a grand total of 27 pairs

Answer 27

oops, forgot 22 and 55, so that's one more pair. grand total: 28 pairs

Answer 28

believe it or not, i just logged on to suggest the same thing :)