Life is A Test 2: Test Harder (Quite A Bit Harder)

by Brony_of_Brody


The Answer 38

The sum is 2178 x 4 = 8712.

We can basically re-write this entire sum as (1000a + 100b + 10c + d) x 4 = (1000d + 100c + 10b + a). Now, let's simplify the entire thing down.

Let's solve a first of all. The left side of the equation is even, so the right hand side must also be even: a multiple of 4. We can also deduce a is even since 1000d + 100c + 10b is also even. That puts a limit on how big a can be, since 4000a must be lower than 9999, because otherwise we'd have a 5 digit number. And the only even number that fits this condition is 2, so a = 2.

Now let's solve d. The left side of the equation is at least 8000 since we now know a is 2, so d must either be 8 or 9. But d cannot be 9, because 4 x 9 =36, and the number on the left side of the equation ends not with 6, but a: 2, in other words. So d must be 9.

Plug both in the formula and it can be revised as: (2000 + 100b + 10c +8) x 4 = (8000 + 100c+ 10b + 2), simplified further as 13b + 1 = c.

Remember, b and c are single digits. c's biggest value is 9, so the biggest value of 2c is 18, so b can only be one, and therefore c is 7.