New Year Cryptogram

Logic Level 1

$\large{\begin{array}{ccccccc} && & & & N & E&W & 1&7\\ +&& & & & N & E&W & 1&8\\ \hline && & & 1& 5 &7&2 &3 & 5\\ \hline \end{array}}$

The above shows a cryptogram, with each letter representing a distinct single digit non-negative integer with $N,E,W > 0$

What is N + E + W ?

25 15 21 18

3 solutions

Ravneet Singh
Dec 26, 2017

Since Last two digits sum is correctly given, therefore "NEW" is added two times and sum is given to be 1572, therefore "NEW" must be 786. Hence N+E+W = 21

S Pranav Kumar
Mar 3, 2018

Assume that upon addition of W and W we get, a 2 digit number x2, where x represents the carry. So we can write , 2W = 10x +2. ......(i) ( Since any 2 digit number xy can be written as 10x +y , where x is the digit in tens place) Now, x + 2E = 10y + 7, ......(ii) where y is the new carry. Similarly , y + 2N = 10z + 5, .....(iii) where in this case z = 1(the final carry). We need to express x,y and z in terms of the given parameters. As, y + 2N = 15, y = 15 - 2N. Substituting this in (ii), we get x +2E = 157 -20N or x = 157 - 20N - 2E Substituting the abve in (i), we get

2W = 1572 -200N -2E or 100N + 10E + W = 786 As N ,W and E represent digits, by observation we can directly say that N = 7, E = 8, W = 6. Therefore N+E+W = 7+8+6 = 21

Pnjjn Pickle
Dec 25, 2017

Let's start with W. The number they add up to is 2, but because the next number (7) is odd, we know that 2 x W = 12. The problem wants 1 x W, so we need to divide 12 by 2. 12/2 = 6. So now we know that W = 6. The same thing needs to be done to find E and W. (17 - 1)/2 = 8, so E = 8. (15 - 1)/2= 7, so W =7. Now, to finish the problem, we need to do N + E + W. 7(N) + 8(E) + 6(W) = 21. So, the answer is 21.

New Year Cryptogram

3 solutions

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