If you cross out the last digit 6 in a three-digit number, the number will decrease by 366. Find this three-digit number.

1. Let’s designate a three-digit number:

x = abc,

where the expression abc does not mean multiplication, but the digits of a three-digit number.

2. If we cross out the last digit ‘c’, then we get a two-digit number

y = ab,

which is less than the original number by 366:

x = y + 366;

100a + 10b + c = 10a + b + 366;
100a – 10a + 10b – b + c = 366;
90a + 9b + c = 366.
3. With a simple selection, we find the digits of the required number:

a = 4;
90 * 4 + 9b + c = 366;
360 + 9b + c = 366;
9b + c = 366 – 360;
9b + c = 6.
b = 0; c = 6.
x = abc = 406.
Answer: 406.