Three people check into a hotel. They pay £30 to the manager and go to their room. The manager suddenly remembers that the room rate is £25 and gives £5 to the bellboy to return to the people. On the way to the room the bellboy reasons that £5 would be difficult to share among three people so he pockets £2 and gives £1 to each person. Now each person paid £10 and got back £1. So they paid £9 each, totaling £27. The bellboy has £2, totaling £29. Where is the missing £1?


Ans:

We have to be careful what we are adding together. Originally, they paid £30, they each received back £1, thus they now have only paid £27. Of this £27, £25 went to the manager for the room and £2 went to the bellboy.

Try to trace the no of eggs

Once upon a time, and old lady went to sell her vast quantity of eggs at the local market.

When asked how many she had, she replied:

Son, I can't count past 100 but I know that.

If you divide the number of eggs by 2 there will be one egg left.
If you divide the number of eggs by 3 there will be one egg left.
If you divide the number of eggs by 4 there will be one egg left.
If you divide the number of eggs by 5 there will be one egg left.
If you divide the number of eggs by 6 there will be one egg left.
If you divide the number of eggs by 7 there will be one egg left.
If you divide the number of eggs by 8 there will be one egg left.
If you divide the number of eggs by 9 there will be one egg left.
If you divide the number of eggs by 10 there will be one egg left.

Finally. If you divide the Number of eggs by 11 there will be NO EGGS left!

How many eggs did the old lady have?




25,201 eggs. This puzzle has a few different methods for finding the solution, one of which is:

Find a number X into which all of the numbers from 2 to 10 divide evenly. You can do this by simply using 2*3*4*5*6*7*8*9*10, but you can find a smaller number by finding the prime factors, a subset of which can be used to form any number from 2 to 10. 2*2*2*3*3*5*7 will do. This comes out to be 2520, and is the lowest number into which all the numbers 2-10 divide evenly.

We can add 1 to this number to satisfy the first 9 constraints of the puzzle (the remainder of 2521/2, 2521/3 ... 2521/10 is one), but this does not satisfy the last constraint, divisibility by 11.

Fortunately, we can multiply X (=2520) by any integer and add 1 and we will still satisfy constraints 1-9. So what Y do we multiply X by so that (X*Y) + 1 is divisible by 11. 2520/11 has a remainder of 1. Thus two 2520s divided by eleven would have a remainder of 1+1 = 2, and so forth...so ten 2520s divided by 11 would have a remainder of 10. This number plus one would divide eleven evenly, as well as also satisfy the first 9 constraints - thus 25201 is the answer.

minimum possible steps: Switching & entering

There are 2 separated rooms, one having 8 bulbs and the other having 8 switches.
You have to find out which switch is of which bulb, in minimum possible steps.
Switching & entering into the room once is defined as ONE STEP



Ans
Since we have 8 bulbs and 8 switches, we only need to find out 7 bulb/switch pairs and then we should know the 8th pair.

With the remaining 7 switches, I choose to switch on two at a time (switching everything else off before each step), like this:

1&2
2&3

And then we should be able to pair switches 1, 2 and 3 to their respectful bulbs with bulb no. 2 being the one lit in both steps and bulbs no. 1 and 3 lit in their respectful steps, and then continue with the same method:

4&5
5&6

Having figured out switches 4,5 and 6 also, we only need to flick switch number 7 to see which one that links to. And as stated previously we should also know by then that bulb no. 8 is the one that was never turned on.

Anybody that can do it in fewer steps?

I'm at work right know, which I should really be getting back to but looking forward to working on a formula for this problem later I'm thinking something - 1, then modulus 3 and then the rest dived by three?


WAIT! - Strike everything above

Having written this post I wondered if turning on three bulbs at a time would work better.... and yeah.... I'm guessing we could do it in 4 steps... :P

Turning on:
Step 1: 1 & 2 & 3
Step 2: 3 & 4 & 5 Giving us the bulb linked to no. 3 (lit first two steps)
Step 3: 5 & 6 & 7 Giving us bulb no. 5 (lit in step 2&3) AND bulb no. 4 (only lit in step 2)
Step 4: 7 & 8 & 1 Same as above, giving no. 6 (only lit in step 3), no. 7 (lit in steps 3&4), no. 8 (the only one first lit in step 4) and bulb 1 (lit in steps 1 and 4)

I could have just turned on switch 7&1 with switch 8 then being linked to the one bulb never lit. Better yet, the same algorithm could be used to link 9 switch/bulb pairs, then with the 9th bulb never being lit.

I then decided to write out the steps in respect to number of odds and even numbers, as so:
1 - odd number 1 = O1
2 - even number 1 = E1
3 - odd number 2 = O2
4 - even number 2 = E2...

With this notation, the steps for the above problem (with 8 or 9 bulbs that is) would be:
O1 & E1 & O2
O2 & E2 & O3
O3 & E3 & O4
O4 & E4 & O1

As some might notice, the number of steps required to pair X switches/bulbs is the same as the number of even numbers counting up to (and including) X. And because an even number divided by two gives us the number of even numbers counting up to that number, all we need to do is to subtract one from the number if X is an odd number, and I would guess the best mathematical notation for that would by x - modulus(x/2), right?

So the the number of steps required to pair X switches to X bulbs is (x - modulus(x/2)) / 2

So, for example, to figure out 13 switch/bulb pairs, we would need:
(13 - modulus(13/2)) / 2
(13 - 1) / 2
12 / 2 = 6 steps

23 Brilliant Doubts - Unanswered

23 Brilliant Doubts - Unanswered


1.If all the nations in the world are in debt(am not joking. even US has got debts), where did all the money go? (weird)

2.When dog food is new and improved tasting, who tests it? (to be give a thought)

3.What is the speed of darkness? (absurd)

4.If the "black box" flight recorder is never damaged during a plane crash, why isn't the whole airplane made out of that stuff? (very good thinking)

5.Who copyrighted the copyright symbol? (who knows)

6.Can you cry under water? (let me try)

7.Why do people say, "you've been working like a dog" when dogs just sit around all day? (i think they meant something else)

8.Why are the numbers on a calculator and a phone reversed? (God knows)

9.Do fish ever get thirsty? (let me ask and tell)

10.Can you get cornered in a round room? (by ones eyes)

12.Why do birds not fall out of trees when they sleep? (tonight i will stay and watch)

13.What came first, the fruit or the color orange? (seed)

14.If corn oil is made from corn, and vegetable oil is made from vegetables, then what is baby oil made from? (No comments)

15.What should one call a male ladybird? (No comments)

16.If a person suffered from amnesia and then was cured would they remember that they forgot? (can somebody help )

17.Can you blow a balloon up under water? (yes u can)

18.Why is it called a "building" when it is already built? (strange isn't it)

19.If you were traveling at the speed of sound and you turned on your radio would you be ! able to hear it? (got to think scientifically)

20.If you're traveling at the speed of light and you turn your headlights on, what happens? (i don have a change to try)

21.Why is it called a TV set when theres only one? (very nice)

22.If a person owns a piece of land do they own it all the way down to the core of the earth? (this is nice)

23.Why do most cars have speedometers that go up to at least 130 when you legally can't go that fast on any road? (stupid, break the law)