There are 17 such numbers.
89.
Let's assume there are 5 total digits, although that would have been handy information to include. All we can deduce from the available information is 4 of the digits. 318_2 There are ten possible digits for the 4th number, leaving 10 possible numbers.
73 84 __________ 292 (multiply 1st number by the unit position digit of 2nd number) 5840 (multiply 1st number by the ten position digit of 2nd number, hence __________ force a zero in the unit position) 6132 __________
29256
There are 17 such numbers.
89.
6210001000
Let's assume there are 5 total digits, although that would have been handy information to include. All we can deduce from the available information is 4 of the digits. 318_2 There are ten possible digits for the 4th number, leaving 10 possible numbers.
1349.
3.
73 84 __________ 292 (multiply 1st number by the unit position digit of 2nd number) 5840 (multiply 1st number by the ten position digit of 2nd number, hence __________ force a zero in the unit position) 6132 __________
29256
For the group of 3 digit numbers : Any number from 1-9 can be the 1st digit, any number from 0-9 can be the 2nd digit, the 3rd digit can only be one number that matches the 1st digit. The number of possibilities is thus, 9 x 10 x 1 = 90. For the group of 4 digits : Any number from 1-9 can be the 1st digit, any number from 0-9 can be the second digit, the 3rd digit can only be the one number that matches the 2nd number, and the 4th digit can only be the one number that matches the 1st digit. Number of possibilities is 9 x 10 x 1 x 1 = 90. Giving a total of 180 palindromic numbers between 100 and 10000.
72
The number 5. See the 2nd related link for more information.
The next digit is 4, followed by 8. Starting from the 1 - each 2nd digit increases by 1 each time. The same is true from the digit 5.