Lines upon Numbers
The 4-digit integer can be written as .
If is equal to another 4-digit integer , what is the value of ?
Try another problem on my set! Let's Practice
The answer is 851.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Note that w x y z = 1 0 0 0 w + 1 0 0 x + 1 0 y + z = a 3 w + b 2 x + c y + d z
That means, a 3 = 1 0 0 0 , b 2 = 1 0 0 , c = 1 0 , d = 1
a = 1 0 , b = 1 0 , c = 1 0 , d = 1
Now, a b c + b c d + a b d + a c d + a b c d + 2 a + 3 b + 4 c + 5 d + a 2 + b 2 + c 2 + d 2
= 1 0 0 0 + 1 0 0 + 1 0 0 + 1 0 0 + 1 0 0 0 + 2 0 + 3 0 + 4 0 + 5 + 1 0 0 + 1 0 0 + 1 0 0 + 1
= 2 6 9 6 = k l m n
k = 2 , l = 6 , m = 9 , n = 6 .
k 2 + l 2 + m 2 + n 2 + 2 k + 2 l + 2 m + 2 n + k l m n = 4 + 3 6 + 8 1 + 3 6 + 4 + 1 2 + 1 8 + 1 2 + ( 2 × 6 × 9 × 6 )
= 8 5 1