I'm posting one puzzle, riddle, math, or statistical problem a day. Try to answer each one and post your answers in the comments section. I'll post the answer the next day. Even if you have the same answer as someone else, feel free to put up your answer, too!

Wednesday, September 23, 2009

How Quickly Can You Do It?

Which is larger: one-third times one-third of a dozen dozen, or one-third dozen halved and cubed?

Slightly different method, same answer: the first one is larger. If you wanted to do it really quickly, the first one is squared before dividing, but the second one is cubed after dividing. I think the time of division is the key.

A mathematician might have generalized and come to the wrong conclusion: If we let X = 12/3, then the two formulas are X^2 and (X/2)^3. For large enough X, the cubed is going to get much larger. But for X small enough, the first is going to be bigger. In this case, X = 4 is small enough for the first to be bigger. As an aside, at X = 8 the two functions are equal.

Enough lecturing... USAF Pilot, Charil and satyrnxoxo had it right. 16 is bigger than 8.

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Math in public...

ReplyDelete1/3 * 1/3 * (12*12)

12 * 12 = 144

1/3 * 144 = 48

1/3 * 48 = 16

[(1/3 * 12) * 1/2]^3

1/3 * 12 * 1/2 = 2

2^3 = 2 * 2 * 2 = 8

So I'd guess one-third times one-third of a dozen dozen

is larger

than one-third dozen halved and cubed.

Slightly different method, same answer: the first one is larger. If you wanted to do it really quickly, the first one is squared before dividing, but the second one is cubed after dividing. I think the time of division is the key.

ReplyDelete(1/3)*(1/3)(12*12)=16

ReplyDelete(1/3)(12)(.5)=8

So the first one would be larger

Wait, the second one should've looked like (1/3)(12)(.5)^3=8

ReplyDeleteA mathematician might have generalized and come to the wrong conclusion:

ReplyDeleteIf we let X = 12/3, then the two formulas are

X^2 and (X/2)^3. For large enough X, the cubed is going to get much larger. But for X small enough, the first is going to be bigger. In this case, X = 4 is small enough for the first to be bigger. As an aside, at X = 8 the two functions are equal.

Enough lecturing... USAF Pilot, Charil and satyrnxoxo had it right. 16 is bigger than 8.