### Brain Teasers

# 3 Digit Number

I am a 3 digit number,

I am evenly divisible by 2, 3, 6, 7,

My 3rd digit is the square root of the 1st digit,

And my 2nd digit is the sum of the 1st and 3rd.

What Number Am I?

I am evenly divisible by 2, 3, 6, 7,

My 3rd digit is the square root of the 1st digit,

And my 2nd digit is the sum of the 1st and 3rd.

What Number Am I?

### Answer

462Condition one:

462/2 = 231.0

462/3 = 154.0

462/6 = 77.0

462/7 = 66.0

Condition two:

The square root of 4 (the 1st digit) = 2 (the 3rd digit)

And finally, Condition three:

4 (the 1st digit) + 2 (the 3rd digit) = 6 (the 2nd digit)

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## Comments

Nice Teaser

100a + 10b + c = x

c = a^1/2

b = a + c

100a + 10(a+c) + a^1/2 = x

100a + 10a + 10c + a^1/2 = x

100a + 10a + 10a^1/2 + a^1/2 = x

110a + 11a^1/2 = x

The only numbers between 1 and 9 that have integer square roots are: 4 and 9.

Inputting 9 yields: 1023 / 2 = 511.5

Therefore the first digit is 4.

c = a^1/2

c = 2

b = a + c

b = 6

100a + 10b + c = x

x = 462

100a + 10b + c = x

c = a^1/2

b = a + c

100a + 10(a+c) + a^1/2 = x

100a + 10a + 10c + a^1/2 = x

100a + 10a + 10a^1/2 + a^1/2 = x

110a + 11a^1/2 = x

The only numbers between 1 and 9 that have integer square roots are: 4 and 9.

Inputting 9 yields: 1023 / 2 = 511.5

Therefore the first digit is 4.

c = a^1/2

c = 2

b = a + c

b = 6

100a + 10b + c = x

x = 462

Oh ya, forgot to include: You don't even need the ramble about what it's divisible by. There are only 2 possibilities with the other criteria, but one of them is a 4 digit number.

Wow, lot of calculations Sane.

By the time I finished reading the teaser I had the answer. There are only three single-digit squares: 1, 4, and 9. Since the middle digit is the sum of the square and it's square root, 9 is eliminated. Since the number is even, 1 is eliminated, leaving only 462.

By the time I finished reading the teaser I had the answer. There are only three single-digit squares: 1, 4, and 9. Since the middle digit is the sum of the square and it's square root, 9 is eliminated. Since the number is even, 1 is eliminated, leaving only 462.

I'll agree with Java. And BTW the so-called answer is not displaying any method for calculating the answer, it only verifies that the answer satisfies the given conditions.

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