Puzzles with numbers and things

[snookersfun]

he could also use the 7th # (5A+8B) for the calculations

[snookersfun]

to make that clear (no editing here ) 7th # x10 + the number by itself, which indeed is much easier.

[davis_greatest]

Congratulations, snookersfun!

Yes, Gordon the gorilla looks at the 7th number in the list and multiplies it by 11. (And multiplying numbers by 11 is very easy, even for gorillas, as you need only start at the end, adding each pair of digits as you work left, remembering to "carry" a 1 when the numbers add up to 10 or more.)

SO HERE IS THE SCOREBOARD AFTER ROUND 20

snookersfun……………………….…..9
Vidas……………………………………….4½
robert602…………………………………4
abextra……………………………..…...3½

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

[Vidas]

Vidas, to what is this referring?

oops. never mind - dropped half of the words in a hurry... (It referred to counting 1's when solving the second problem (i.e. #20)).

[davis_greatest]

Rounds 21 and 22 - Oliver and Gordon have some fun

After today, I shall not be able to go online for a little while. So here are some games that Oliver and Gordon like to play. They play a different game every day of the week. Below are the games they play on Monday and Tuesday.

If these are solved quickly, I may try to post later today something more challenging!



Question 21 - Monday’s game

Gordon and Oliver play a game. Oliver can choose any 17 numbers he likes and write them on the blackboard. Gordon can then choose 5 of them – if he can find 5 numbers that add up to a multiple of 5, he wins. If he cannot, Oliver wins.

For example, if Oliver chooses 1, 2, 3, 4, 10, 15, 20, 25, 30, 35, 40, 45, 50, 77, 99, 100, 1531, then Gordon might choose 3+20+25+30+77 = 155, which is a multiple of 5, so Gordon would win.

They are both very clever and will always choose numbers in the best possible way. If Oliver can choose numbers that will make it impossible for Gordon to win, he will do so. But if Gordon can win, he will. Who wins?



Question 22 - Tuesday’s game

On Tuesday, Gordon can choose any 10 different numbers below 100. If Oliver can pick from these any two different selections (of as many numbers as he wishes, as long as he picks at least one number) which add up to the same total as each other, Oliver wins. If he cannot, then Gordon wins.

For example, if Oliver chooses 1, 2, 3, 4, 5, 6, 7, 8, 9, 21:

then Gordon might choose 2+3 which adds up to 5, as his first selection; and might choose 5 on its own (which also has total 5) as his second.

Or he might choose 5+8+9 which adds up to 22 and might choose 1+21. So Oliver would win.

As always, they are both very clever and will always choose numbers in the best possible way. Who wins?




Note:
“Numbers” above always means “positive integers, i.e. whole numbers greater than zero: so 1, 2, 3, …” This is because Gordon and Oliver don’t yet understand other sorts of numbers. (Charlie can recite pi to 85,000 decimal places and calculate in his head the complex roots of any quadratic, cubic or quartic equation, but he is cleverer than my other two pets.)

[Vidas]

Re: question 21-
Gordon can probably win, as he
can pick either 5 numbers of the same kind -
5a+k, 5b+k, 5c+k, 5d+k, 5e+k (same remainder)
or (if there are less than 5 numbers for any k=1,2,3,4,0)
there should be 5 numbers with 5 different remainders(17>4x4)
5a+1, 5b+2, 5c+3, 5d+4, 5e.
(their sum is a multiple of 5 too).

[davis_greatest]

Congratulations, Vidas!

SO HERE IS THE SCOREBOARD AFTER ROUND 21

snookersfun……………………….…..9
Vidas……………………………………….5½
robert602…………………………………4
abextra……………………………..…...3½

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


Round 22 is still open.

[snookersfun]

After today, I shall not be able to go online for a little while.

Hope the absence won't be too extended. Will miss you, what shall we do without the daily challenges.
At least, I'll get something done at work

[The Statman]

What about if Gordon chooses:

99 97 94 90 85 79 72 64 55 45

[Vidas]

then Oliver picks 85+79 and 64+55+45...

[davis_greatest]

Yes, he could. But of course Gordon might not choose those numbers. The question is still open...

[PaulTheSoave]

I presume Gordon does everything on a snookertable regarding the title of this thread, Snooker quizzes.

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]

I presume Gordon does everything on a snookertable regarding the title of this thread, Snooker quizzes.

Of course he does! I originally put this thread in the Off Topic section. Robert602 (at least, I think it was he) later moved it here to the Snooker Quizzes section - take it up with him if you don't like it. Oliver and Gordon are remarkably adept at snooker, if that helps!

PS The title of this thread is "Puzzles with numbers and things", not "Snooker Quizzes".

[PaulTheSoave]

I like those puzzles and the wizkids grinding on it, just banter

[davis_greatest]

I like those puzzles and the wizkids grinding on it, just banter

I know! If you like good banter, though, you should try talking to Charlie.