On January 8th of this year Bobby Fischer won the U.S chess championship for the first time. He was only 14 years old. During that same year he...

Let the year be represented by abcd where a is in the thousands place, b is in the hundreds place, c in the tens place and d in the units place.

We are given that bxd=72 (hundreds digit times unit digit is 72). And we are given that the hundreds digit is 1 more than the units digit so b=d+1. Then b=9 and d=8. (You can get this by guess and check: 5x4=20,6x5=30,...,8x7=56,9x8=72) or if you have algebra:

d(d+1)=72 ==> d^2+d-72=0 ==> (d+9)(d-8)=0 ==> d=8 (since d>0)

Also c=5 since the number of sides of a pentagon is 5.

The sum of the digits is one less than 2 dozen or 24-1=23.

So a+b+c+d=a+9+5+8=23 ==> a=1

The year was 1958