Question

Question #6f35a

Answer 1

6116

Explanation:

to have a number read forward and backward the same, it must contain only 1 or 2 different numbers

ABBA or AAAA

since the sum of the numbers is 14
`14/4=3.5`
The answer is not a complete/integral number
Thus there are two different numbers in the number set.

let the numbers be x and y
`2x+2y=14`
`2(x+y)=14`
`x+y=7`

since rounding it to nearest thousandths gives 6000,
the number pairs can be:
- 5 as the first and last number and a number greater than or equivalent to 5 (5-9) as the two middle numbers
- 6 as the first and last number and a number smaller than 5 (0-4) as the two middle numbers

let `x=5 and 6 respectively`
`5+y=7`
`y=2`
2 is not greater than or equivalent to 5

`6+y=7`
`y=1`
1 is smaller than 5

Confirm that the numbers are 6 and 1
with the arrangement
`6116`