FORTNIGHT'S PUZZLE 8

PUZZLE 8: 25th-31st January (to be e-mailed by the 1st February)
POSTED BY IES CAMPANAR

DIGIT NUMER
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, 3The digits in the middle are: 6, 7 or 2,9There are eight possibilities, the numbers: 2673, 2763, 3672, 3762, 2293, 2923, 3292, 3922The solution is the number: 3762 (because 3762-1089 = 2673)