### Brain Teasers

# Squares and Cubes and Squares

1) There is only one 2-digit number that is both a square and a cube. What is it?

2) There is only one 3-digit number that is both a square and a cube. What is it?

3) Which 3-digit number, made of consecutive digits, is 2 less than a cube and 2 more than a square?

4) What 2-digit number is 1 more than a square and 1 less than a cube?

2) There is only one 3-digit number that is both a square and a cube. What is it?

3) Which 3-digit number, made of consecutive digits, is 2 less than a cube and 2 more than a square?

4) What 2-digit number is 1 more than a square and 1 less than a cube?

### Answer

1) 64;8 times 8 and 4 times 4 times 42) 729; 27 times 27 and 9 times 9 times 9.

3) 123 is two more than 121(11 times 11) and two less than 125(5 times 5 times 5)

4) 26 is one more than 25(5 times 5) and one less than 27(3 times 3 times 3)

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## Comments

some square thought that up.

Iam no math brain you cant fool me!m

to ignorant. ha ha

Iam no math brain you cant fool me!m

to ignorant. ha ha

did not even try this one, way to hard, ship it off to the math department.

Ha ha, I'm no square. 12 years old.

Good job Tammy!

Does anyone mind if I add another question to the teaser?

i got it i am sooo good

This does not belong in the logic section. It should go in the math section.

Tammy i am 13 and i am completly confused are you even still in elemantry/middle school? If you think i am stupid you may be right.

I'm in, or was, in 6th grade, but skipping 7th grade math. Going to 8th grade honors algebra next in september. I doubt that you're stupid. Nobody is, really. Don't think so harshly of yourself.

This was fun though I must admit that i have to use excel to work this out (to lazy to compute manually )

Hey that was really cool. I used to do that stuff in my gt class.

i wonder why ppl find it so tough.it took me 1/2 minute to figure all the 4 answers.I admit that I already knew the 1st two answers and next two can be easily figured out as 123 is the 1st three digit no. with consecutive digits and 27 is the first two digit cube.so just by trying the first possible cases you get the result.

The book is titled Mathemagic.

Cute, but pretty easy, especially when you consider that there are only seven 2- or 3-digit cubes.

A number that is both a square and a cube is the square of a cube (or the cube of a square). Thus the first three are: 1^6 = 1, 2^6 = 64 and 3^6 = 729. That part of the teaser was rather elementary.

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