The mysterious number
Number Theory
Level
1
When I was walking on the road, I saw a car coming nearby which had a four digit number in which the middle two digits were the same. Its unit's digit was the product of the middle two digits and the sum of all the four digits was 23. Find the number
The answer is 8339.
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Let the number be abbc, with a,b,c between 0 and 9.
We are given:
a+2b+c=23 and c=b^2
Clearly, b=0,1,2 or 3 and c=0,1,4, or 9 (respectively)
The only one of these which satisfies a less than or equal to nine is b=3, c=9, a=8