# Ok here's another one for you brainiacs...

By kainoa ยท 21 replies
Oct 24, 2002
1. Three men check in at a motel. The rate is \$30 so they split it evenly \$10 ea. Later, the manager remembers the rate is only \$25 so he sends a bellboy up to their room with the difference. However, the bellboy realizes he can't evenly split the \$5 three ways so he keeps \$2 and gives the men back \$1 each. So \$9x3=\$27+\$2(bellboy)=\$29...where did the other \$1 go!?

2. ### Phantasm66TS RookiePosts: 5,734   +7

Is this the best you can do????

You are adding up the wrong numbers. You are assuming that these numbers must be added to reach 30 when in fact they should equal 25 with a subtraction. They payed nine dollars each with the refund, and they never knew that other two dollars were refunded, so you have 27 dollars paid plus a 3 dollar refund = \$30. The other two bucks are insignificant, and not necessary to add to the total. The two bucks bit is just put in to throw you off the scent and detract from the logical certainty that a whole single digit 1 cannot disappear magically from a sum. That's impossible.

30-5=25 25+2(bellboy)=27 27+3(refund)=30
9*3=27 27+3=30.......easy

3. ### Julio FrancoTechSpot EditorPosts: 7,330   +775

Ahhh... after 10 minutes of brainstorming I couldn't get a clear solution, I knew something was missing, but anyway, I was so mad about it I just had to Google it

I was about to post the answer here as a reply but then I thought it would be much more fun if you guys can have a clear attempt on solving the problem, if you get too frustrated, here you are: MathForum.

Nice post, too kainoa, welcome aboard and keep em coming.

4. ### Julio FrancoTechSpot EditorPosts: 7,330   +775

Heh, you either knew the problem from somewhere else or are too smart for me... maybe I could have spent some more time trying to solve it but I get kinda frustrated too fast :blackeye:

5. ### Phantasm66TS RookiePosts: 5,734   +7

Here's where I come clean and say that I have worked out this problem before a while ago. The trick is more in the wording than anything else as when you follow the calculation at the end you see that its totally nonsense and not a representation of what happened.

6. ### Phantasm66TS RookiePosts: 5,734   +7

OK, here is a pretty easy one:

What comes NEXT in this sequence:

1,2,3,5,8,13,??

...Oh, and WHY???

Each following number is the last two numbers added together...
Like you said - Easy...

But i still can't get my head around that first one

8. ### Phantasm66TS RookiePosts: 5,734   +7

So the next number IS????

21.

The first one is not as hard as it looks. Try to ignore the calculation bit here:

So \$9x3=\$27+\$2(bellboy)=\$29...where did the other \$1 go!?

Which is basically crap and not what happened. Don't look at that bit of the riddle, its put in to confuse you.

9. ### Julio FrancoTechSpot EditorPosts: 7,330   +775

Go to that link I posted before, good explanation with the table and all that, but like P66 said once you look at it clearly, it's not much of a math trick (the way I was trying to look at it) but rather a wording thing, a very tricky wording thing

10. ### LNCPapaTS Special ForcesPosts: 4,243   +446

The reason the first one looks messed up is because the \$25 rate couldn't be split into 3 evenly. 24 is the nearest integer divisible by 3. Each man should actually be paying out \$8.33 1/3

LNCPapa

11. ### Phantasm66TS RookiePosts: 5,734   +7

I thought that originally too, but the answer isn't in thinking in terms of split dollars....

Try forgetting that the bellboy is in the question and that the whole bill is \$27 instead of \$25. That bit is stuck in to confuse you. They each got \$1 back. 3 x \$1 = \$3 plus \$27 = \$30.

The sum at the end is WRONG but its set up in a way that looks right but isn't. That sum does not express what happened in this transaction.

Instead of reading the question the way its phrased, try thinking about what actually happened. The question is phrased in a way that's deliberately confusing, and then the sum at the end is pretty much a load of crap. Its not adding the correct numbers together, and so its producing a wrong total.

12. ### kainoaTS RookieTopic Starter

Nice try guys. Took me a while to figure this one out myself. How long did it take you 66 (when you tried it the FIRST time)?

As for the still confused the clearest explaination I can give is that when the bellboy takes the \$2, the total amount the men pay for the room actually becomes \$28 or \$9.33ea (NOT \$27 as does the riddle falsely imply).

:grinthumb

13. ### Phantasm66TS RookiePosts: 5,734   +7

I knew that the answer obviously wasn't right so I drew out on a piece of paper what was happening and realised that it was very simple. Probably about 5 mins or so....

14. ### kainoaTS RookieTopic Starter

HEHE...i drew it out too but i still couldnt see it!

Ok, heres a nice one for you

For a closed set of numbers,{1-20}

8, 18, 11, 15, X, 4, 14, X, 19, X, 7, 17, 6, X, 10, 13, 3, X, X, 2

Place the following numbers into the proper order within the sequense.

1, 5, 9, 12, 16, 20

You'll have to think "outside the box" on this one.

16. ### GoalieTS BoosterPosts: 616

Easy:

8, 18, 11, 15, 5, 4, 14, 9, 19, 1, 7, 17, 6, 16, 10, 13, 3, 12, 20, 2

Not quite outside of the box. Maybe written on it though.

Yeah writing it down helps a lot

18. ### Phantasm66TS RookiePosts: 5,734   +7

Think about what REALLY happened and you will realise that its simple.... 30 minus 27 is 3....

19. ### JustinTS RookiePosts: 942

'

13 + 8 is 21...

21 + 13 is 34...

fibernaci(?)s golden ratio

20. ### SNGX1275TS Forces SpecialPosts: 10,729   +409

Thought RustyZip already covered that one soul

21. ### JustinTS RookiePosts: 942

let me rephrase...

Is that not the fibernaci sequence of repetition in nature? I forget.

22. ### SNGX1275TS Forces SpecialPosts: 10,729   +409

oh, I know that sequence, well I don't know it but I've heard of it and been taught it once... and the spellings I thought of trying to figure out how to google it arent any better than yours so I'm not even goign to try to google it.