Any maths teachers on this forum?

One possible solution would be

11x11 = 121 so quoting "4" is plainly "wrong"

22x22 = 484 so quoting "16" is plainly "wrong"

33x33 = 1089 so quoting "anything other than 1089" is plainly "wrong" and therefore a "valid" solution

There are quite a few other "valid" solutions.

Oooh err missus.

I recal at university, one lecturer asking us for the next number 1, 2, 4, 8, 16, 32.................

Most of us opted for 64.

"Nope !" said the lecturer. "Each number in the sequence is simply "numerically bigger" than the preceding one, so any number 33 or larger will do !"

Not everything is logical or "bleeding obvious" - says a lot about this forum.......................

I can see his point, it was a clever example and it reminds me of a story:-

A Biologist, Physicist and Mathematician were traveling by train to Scotland and had just crossed the border.  The Biologist looks out of the window and sees a field with a single black sheep in it but no other sheep.  "Look," said the biologist "all of the sheep in Scotland are black."

The physicist chuckled and said "No we can say that some of the sheep in Scotland are black."

But the mathematician said "No, all you can say is that in Scotland there is a field with one black sheep in it."

btw your lecturer did not give enough information for you to make a decision, as our train-bound mathematician would have said.

We can either assume there is no pattern in which case we cam make up an answer or assume that there is a pattern. If the latter is the case I'm going for 18.  This is on the basis that:

11x11=121 add up the numbers in the answer >4

22x22=484 add up the numbers in the answer >16

33x33=1089 add up the numbers in the answer >18

What function produces a infinite list starting with  1, 2, 4, 8, 16, 32, 33....

.............I don't know............but it must have sort of discontinuity.

Nice story BB. I have modified it slightly......................assuming that the sheep didn't turn around whilst the train was passing....................

Yep ! there are quite a few "valid" solutions. All of which depend on a specific assumption. None of the assumptions are inherant in the question.

Your's is a common, and very good answer. If the original list had been extended to 33x33 = 1089, and asked for 44x44 = ? an answer of 19 might be justified.

I was hoping for a logical answer and so I am sticking to 36!  I am unanimous about this.

That's it take it to the nth degree.

What's the probability of three people when asked to add 8 numbers together all come up with the SAME incorrect answer.

Answers must be obtained without the use of an Infinite Improbability Drive.

On this forum...............1............. ie a dead cert.

But more interestingly what (exactly) does that prove ?

But can we use the Bistro Drive to make a quick getaway?

I hope this lecturer was not in the department of mathematics.  A sequence presented in that form can only have one correct number for subsequent elements and it has to be 64.  What he gave you is just a list of numbers.

Precisely. And although we all thought he had given us a mathematical sequence, hence our "64" answers, he hadn't.

Now "h" has simply copied an array of numbers without providing any clue as to whether it is a functional series or some "process-following" sequence" or anything else. So there is no justification for assuming the "genius solution" that is requested has to be based on a mathematical function.

Now, I have written a little spread sheet to generate the 11x11 = 121 = 1+2+1 = 4 type solution, but I think this is more like a "process-following" sequence rather than a mathematical series. However, as I said before, there are quite a few process sequences that can be generated, from the limited information in order to predict 33x33, 44x44 etc. But note, the supplied information doesn't even predict that 44x44, or 55x55 etc are the next inputs to the sequence.

I basically agree with you Kevin but I think the Maths lecturer was trying to make a point.  Yes it would seem the only correct value would be 64, where the next value in the series is given by 2n, where n is the previous value or the sum of all previous values +1 - they are both the same because we are looking at base 2 number property.  But can you be 100% sure that there is no other function that could give those 1st 6 values?  The thing in Maths is that you have to tie everything down and if you don't you can get into serious trouble.  Read the book by Andrew Wiles to see what I mean, he was all ready to publish his proof of Fermat's last theorem and realised he had not got everything tied down.

I think that basically this maths lecturer was saying not to take anything for granted.  I think my 3 geezers on the train is a better example though.

I like your solution - it works for 11 * 11 and 22 * 22 but gives a different value to my solution for the 3rd term.  So if we an find two different 3rd sequence members then all we can say is that we don't have enough information to crack the sequence - so basically I agree with you we need more.

Perhaps "h" could enlighten us all as to what he had in mind when he requested a "genius" solution ?

Zero (0)!

You must have gone to a different school of psychology than me..............

Err no it ain't.  It may be low but you ill have to prove it is zero.  I bet old Heisenberg is turning in his grave right now.

I'll drink to that! HIC!

Why the need to prove anything? The question says 'SAME incorrect answer'. As the people are free to choose their numbers then sum them, there's no such thing as an incorrect answer therefore no chance whatever of any coincidence of incorrect answer.

No permutation or combination of numbers is incorrect (that's how I see it anyway) 

Huh? I'm not sure if you're deliberately misunderstanding the question. The point is that there is a pattern to those particular numbers that regulalrly causes people to get the sum wrong (i.e. an "incorrect answer") if they are too hasty in their mental arithmetic. The odds that people will get the sum of THOSE numbers (presented in that particular way) wrong in an identical fashion (incorrect 5000 Vs the correct 4090) are much higher than for a random set of numbers. But even for a random set of numbers, there is a finite, but low, probability that identical errors will be made by different people when summing them.