Question #6f35a

1 Answer
HCH
Jul 12, 2017

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#

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