SOLUTION: what is the number that satisfies the following three conditions ? It is an integer greater than 999 and less than 1,234 The sum of its digits is 14 Its tens and units di

Question 305809: what is the number that satisfies the following three conditions ?
It is an integer greater than 999 and less than 1,234
The sum of its digits is 14
Its tens and units digits are the same

Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
First digit is 1.
Last two digits are the same. 11,22,33,44,55,66,77,88,99,00
The sum is 14.
The sum of the first (1) and last two (from above) is 3,5,7,9,11,13,15,17,19,1
The hundreds digit must be between 0 and 9.
Look at the sums and throw out any less than 5 (5+9=14) and greater than 14.
That leaves five possible combinations: 5,7,9,11,13.
For each of these to make 14 the final digit must be 9,7,5,3,1
Match up the sums with the appropriate two last digit pairs, 5 (with final digit 9) goes with the 22 pair
1922
1733
1544
1355
1166
The last limit is the number needs to be between 999 and 1234.
1166 is the number.
RELATED QUESTIONS
a three-digit number satisfies the following conditions: the digits are consecutive whole (answered by MathTherapy)

a three-digit number satisfies the following conditions: the digits are consecutive whole (answered by J2R2R,poliphob3.14)

The sum of three odd consecutive integers is less than 100. Find the largest integer that (answered by stanbon)

Three-fifths of a number is greater than two-thirds. Find the smallest integer that... (answered by chitra)

Here is a divisibility puzzle find a number of that satisfies the following conditions A (answered by richwmiller)

Identify the number that satisfies all three of the following conditions:  it is (answered by josgarithmetic,119078)

Identify the number that satisfies all three of the following conditions:  it is (answered by josgarithmetic,MathTherapy)

a is an integer that is greater than 2. If x is a real number that satisfies the equation (answered by KMST)

find three consecutive integer such that twice the greater integer is 2 less than 3 times (answered by CubeyThePenguin)