WEEK'S PUZZLE 8

PUZZLE 8 – from the 23rd to the 29th of November ( to be collected by the 30th of November)

A certain four-digit number obeys the following conditions:
a) The sum of the squares of the two digits on both sides is = 13.
b) The sum of the squares of the two digits in the middle is =85.
c) If we substract 1089 from that certain four-digit number, we get another figure this time with the same digits but exactly in the opposite order.
Which number is it?


SOLUTION
Because of the conditions:
The digits on both sides are: 2, 3
The digits in the middle are: 6, 7 or 2,9

There are eight possibilities, the numbers: 2673, 2763, 3672, 3762, 2293, 2923, 3292, 3922

The solution is the number: 3762 (because 3762-1089 = 2673)