Lockers are numbered with consecutive positive integers beginning with 1, and the digit 2 is used exactly 106 times (including on the last locker). what is the number of the last locker?

250

Step-by-step explanation:

I guess you could say use casework to solve this problem. You can go through numbers 1 - 99 to find the digit 2 appears 20 times, 10 times in the units digits, 10 times in the tens digit. Let's proceed to 100-199, where you see, again, 2 appears 20 times. 20+20=40 times already. We need 66 more numbers. Well, since now we're in the 200s, each number has a 2 located in it. 199+66=250

a² + b²= c²

24² + 7² = c²

c= 25

b.an increase in a causes b to decrease