### Brain Teasers

# Powers of Four

Sally and Anna took turns multiplying numbers. Sally picked the number four. Anna multiplied that by 4 to get 16. Sally multiplied that by 4 to get 64. Anna multiplied that by 4 to get 256.

After going back and forth several times, one of them got the number 1,048,576. Who came up with that number, Sally or Anna?

After going back and forth several times, one of them got the number 1,048,576. Who came up with that number, Sally or Anna?

### Hint

You may be able to find a pattern!### Answer

Anna came up with that number. Note that all of Anna's numbers end in 6 and all of Sally's numbers end in 4. That's all you need to know!Hide Hint Show Hint Hide Answer Show Answer

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## Comments

The problem here is that it is all to easy to just keep multiplying by four, and you STILL get the right answer...hmm....

Great Riddle, but very easy.

Well now you have shown me an easy way it's easy but I found that the number was 4^10 which is an even power of 4. I like your way better! Good puzzle!

I could only work it out the long way- I didn't notice the last numbers.

I still think you didn't need the hint though.

I still think you didn't need the hint though.

Thank you all, I know it's kind of easy, but anyways... ;)

Sep 23, 2003

Just a thought...who here thinks Sally and Anna need to get a life?

I do, I do!

come on! It's just a riddle!

Good one! I agree that they need to get a life LOL.

I also tried to explain to my students (middle school) that I got the answer by dividing 1,048,576 by 4 gives you 262,144 and because this ends in an even number, you can assume that Anna, the 2nd person, was the one to get that answer.

I also tried to explain to my students (middle school) that I got the answer by dividing 1,048,576 by 4 gives you 262,144 and because this ends in an even number, you can assume that Anna, the 2nd person, was the one to get that answer.

Thanks. You teach middle school? I don't believe that, because I am soooooo much younger than that! Am I suppose to be on this site?

This teaser is so lame so boring and so easy. Try making your teasers a bit harder.

wowzers, mega harsh there timmyboym, criticism is good, so long as it be constructive, that was just rude. as for the teaser, i am lame when it comes to math, i thought it was good.

Thanks a bunch blushinglily83!

(ln 1,048,576)/(ln 4) = n

if n/2 is a whole number - Anna came up with that number.

if n/2 is a whole number - Anna came up with that number.

You should have used a number like 4^30. Then it would have taken me three times as long, and when you revealed the simpler way to figure it out, I'd have smacked my forehead three times as hard!

This was from that book Mathemagic.

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