Puzzles with numbers and things

[davis_greatest]

Eh?

wouln't say the second is that easy to count.

Vidas, to what is this referring?

[davis_greatest]

Good answer, Vidas!

wouln't say the second is that easy to count.

- If Gordon mastered fractions, - he would simply write 1/17 (nobody said it's an integer number?)

n- number you choose, A- Gordon writes on your forehead
- When you choose Olivia/Elizabeth/Naomi n=1,8,9 the final number n*17*A should consist only of 1's/8's/9's. The smallest number like 11...11 that can be divided by 17... 1111111111111?(16 1's).
Then A=11..11/17=65359477124183(we ran out of spaces in Excel again).
A*n*17 =nn....n.
If Gordon has neat handwriting, he'll manage to put it on your forehead.
but it's still big number. Any other suggestions?

Another point for you! Well done, Vidas! I should have added that it must be a whole number, but I thought it would be obvious. He doesn't understand fractions - he's a gorilla, not a maths professor (or Charlie)!

We note also that 0.111111.... = 1/9,
so your number 65359477124183 is composed of the first "16"* digits in the decimal expansion of

(1/9) / 17

= 1/153 =

0.00 65359477124183 00 65359477124183 00 65359477124183 ...

* This can be looked at as a 16-digit number starting with "00". Clearly, we can ignore the initial "00" so get a 14-digit number.

This puts you up to 2nd place!

SO HERE IS THE SCOREBOARD AFTER ROUND 20 BUT WITH ROUND 19 STILL ALIVE

snookersfun……………………….…..8
Vidas……………………………………….4½
robert602…………………………………4
abextra……………………………..…...3½

(once round 19 is complete, scoreboard will add up to number of rounds+1 since 2 members each got a point for round 14)

[davis_greatest]

the whole addition is basically made up of the same two initial numbers (e.g. the third # is the sum of A+B, the 4th then A+B+B...), if you add all those #s up, you will see, that the final sum of all ten #s is made up of 88B+55A. As Gordon has mastered the x11 tables, he shouldn't have a problem calculating that quickly.

You're about halfway there. But even with his mastery of the 11 x tables, calculating 88B+55A in his head so quickly is too hard for Gordon. So how does he do it that makes it much easier than this?

[Vidas]

Re: Question 20

wouln't say the second is that easy to count.

- If Gordon mastered fractions, - he would simply write 1/17 (nobody said it's an integer number?)

n- number you choose, A- Gordon writes on your forehead
- When you choose Olivia/Elizabeth/Naomi n=1,8,9 the final number n*17*A should consist only of 1's/8's/9's. The smallest number like 11...11 that can be divided by 17... 1111111111111?(16 1's).
Then A=11..11/17=65359477124183(we ran out of spaces in Excel again).
A*n*17 =nn....n.
If Gordon has neat handwriting, he'll manage to put it on your forehead.
but it's still big number. Any other suggestions?

[snookersfun]

that's too easy

the whole addition is basically made up of the same two initial numbers (e.g. the third # is the sum of A+B, the 4th then A+B+B...), if you add all those #s up, you will see, that the final sum of all ten #s is made up of 88B+55A. As Gordon has mastered the x11 tables, he shouldn't have a problem calculating that quickly.

Having mastered his 11 times tables during the previous question, my pet gorilla Gordon likes to show off, pretending that he is cleverer than he really is and trying to compete with my even cleverer pets Oliver and Charlie. Gordon likes to do the following trick.

He will shut his eyes and ask my pet orang-utan Oliver to write any number he wants on our blackboard and then my pet chimpanzee Charlie to write any number below it.

Then, while Gordon still has his eyes shut, I have to write below Charlie's number a 3rd number on the board which has to be the sum of Oliver's and Charlie's numbers. Then I must write a 4th number, which must be the sum of the 2nd and the 3rd, and I must keep writing numbers, each time the sum of the two above, until there are 10 numbers on the board.

Once I have finished, I must say so and Gordon will open his eyes and glance momentarily at the board. Immediately, he will write on the board the sum of all ten numbers.

Now, we all know that he is not that bright to add up these numbers so quickly. Charlie could, but Gordon, no way. So, how does he do it?

[davis_greatest]

... and round 20 too - Gordon gets smart

I won't be around till tomorrow night, so I'll set another one now - hopefully having two to work on will keep you quiet.

Question 20 - Gordon gets smart

Having mastered his 11 times tables, Gordon is getting smarter by the day. He's now up to his 17 times tables, and may soon be challenging Oliver in the smartness league. He's also been meeting more girls - not only Florence, Elizabeth, Sylvia and Talia, whom you have met before, but he now also talks a lot on the phone to Olivia and Naomi.

He also still likes dazzling us with tricks. Here is his latest one:

Gordon writes a number on my forehead, which I cannot see. I can then choose any of his lady friends, choose any number from one to nine with the same first letter as the girl's name, and multiply it by 17. I then have to tell Oliver the number I arrive at, and he will multiply it by the number written on my forehead. He will then tell me the answer and it turns out that the first letter of every digit will be the first letter of the girl's name I thought of!

For example, say Gordon had written 8 on my forehead and I had then chosen Florence. I then choose number 4, say, beginning with F (for four). I multiply it by 17 to get 68. Oliver multiplies this 68 by the 8 on my forehead to get 544 - Five Four Four, each digit starting with F for Florence!

However, had I chosen Elizabeth, for example, this would not have worked. Therefore, Gordon could not have written 8 on my forehead.

Gordon always wants to write the smallest number he can. So what does he write on my forehead?

[davis_greatest]

Round 19 - Gordon shows off

Having mastered his 11 times tables during the previous question, my pet gorilla Gordon likes to show off, pretending that he is cleverer than he really is and trying to compete with my even cleverer pets Oliver and Charlie. Gordon likes to do the following trick.

He will shut his eyes and ask my pet orang-utan Oliver to write any number he wants on our blackboard and then my pet chimpanzee Charlie to write any number below it.

Then, while Gordon still has his eyes shut, I have to write below Charlie's number a 3rd number on the board which has to be the sum of Oliver's and Charlie's numbers. Then I must write a 4th number, which must be the sum of the 2nd and the 3rd, and I must keep writing numbers, each time the sum of the two above, until there are 10 numbers on the board.

Once I have finished, I must say so and Gordon will open his eyes and glance momentarily at the board. Immediately, he will write on the board the sum of all ten numbers.

Now, we all know that he is not that bright to add up these numbers so quickly. Charlie could, but Gordon, no way. So, how does he do it?

[snookersfun]

I really should check out the first few questions then. I only remember looking at them then and being scared away from the thread. But that anyway is the problem with math, it always looks so complicated until you find a good starting point.
OK, off for today, have to give up the computer and the kids can't understand, why I should want to solve math-puzzles

[davis_greatest]

btw. what ever happened to Robert. I have a feeling, he could lead this easily.

I think he's away for a bit. Will be good to see how things go when he's back... I think the recent questions have been more difficult than the first few. What do you think?

[snookersfun]

btw. what ever happened to Robert. I have a feeling, he could lead this easily.

[snookersfun]

PS Remember the rule of no editing of your answers! I was lenient this time, and didn't disqualify you!

I only edited the colors, the yellow was awful to see.
Anyway, it was only in the explanation, so I thought it's OK. Will not edit anymore then. Or maybe you think about a new rule, as explanations sometimes need some editing to be clear (similar to your questions)
Had someone come up with an explanation before my edit, you could have given him the point though...

[davis_greatest]

PS Remember the rule of no editing of your answers! I was lenient this time, and didn't disqualify you!

[davis_greatest]

Well done, snookersfun!

Good answer! Pulling away at the top of the scoreboard. Isn't Charlie clever? Beware if he starts setting the questions - they could get a lot harder!


SO HERE IS THE SCOREBOARD AFTER ROUND 18

snookersfun……………………….…..8
robert602…………………………………4
abextra……………………………..…...3½
Vidas……………………………………….3½

(scoreboard adds up to number of rounds+1 since 2 members each got a point for round 14)

[snookersfun]

oops: Sylvia of course (Elizabeth was out for a while)

[davis_greatest]

Ok, here it goes:
possible answers are: 23,21 - 34,32 - for Talia (brunette followed by blond)
45,43 - 56,54 for Florence; 67,65 -78,76 for Sylvia and 89,87 for Elizabeth.

Now, Oliver, which knows, the last digit, initially has no idea, which haircolor she has, therefore he wasn't told the digits 1,2,8 or 9 (which appear only once in the above list).

Even after getting that piece of info DG doesn't know either, it follows, that he didn't have the first digit of 2,3,7 or 8 (which were left with one option each).

Meanwhile we are left with 45,43 - 56,54 for Florence and 67,65 for Sylvia.
Oliver didn't have the last digit of 5, the only ambiguous answer left to him, as the answer was clear to him now. He also shouts out a haircolor, which fits only one girl, otherwise Charlie couldn't have named the girl. Therefore he must have shouted out 'blond' (Had he shouted brown, either Flo or Eli had been possible.)

Just correct one of the last 7 words and the point will be yours!