Seven oaks question

[Sulikhan]

18)
In the sum below the letters J,M and C represent three different zero.
What is the value of J+M+C?

J J
M M
C C
---------
JMC


ANSWER IS 18

[solimum]

This is a fiddly one and I think it needs some trial and error

First notice that the three 2-digit numbers which are added together must all be in the 11 times table. So the sum must also be in the 11 times table

JJ = 11 x J
MM = 11 x M
CC = 11 x C

JMC = 11 x (J+M+C)

So the easiest way is to make a list of the first few three digit multiples of 11, add up the digits and see if they match the multiple

So 132 = 11 x 12 1+3+2 = 6 so this doesn't work
143 = 11 x 13 1+4+3 = 8

Try the next few until

198 = 11 x 18 1+9+8 = 18 RESULT!!

[Mitumum]

J J
M M
C C
---------
JMC

From the first column, it is clear that J+M=10
From the second column, it is clear that M=C+1
From the third column, it is clear that J=1

so , M=9, C=8
J+M+C=1+9+8=18