Puzzles with numbers and things

[snookersfun]

Congratulations:

Round 25, Vidas!
Round 26, snookersfun!
and most of all, Round 25½, davis_greatest! (half rounds are worth 2 points)


HERE IS THE SCOREBOARD AFTER ROUND 26

snookersfun……………………….…..13
Vidas……………………………………….7½
robert602…………………………………4
abextra……………………………..…...3½
davis_greatest…………………..……2

(some rounds may be worth more than one point)
(especially ones won by davis_greatest)

DG, how about giving points for each problem put up (by DG) + each hint

[April madness]

(some rounds may be worth more than one point)
(especially ones won by davis_greatest)

I still remember you promised to give me 10 points on this quiz!

[davis_greatest]

I still remember you promised to give me 10 points on this quiz!

For 10 points, you'd need to do my ironing!

[April madness]

For 10 points, you'd need to do my ironing!

hmm. I am definitely starting to forget everything, I thought you'd do my ironing and give me 10 points for that

have to think now.

[davis_greatest]

Question 27 - Chessboard madness

I had a few euros left from my holiday so I decided to invest the money by placing it on a chessboard. The best way, I have found, to guarantee good returns is to place some money in each square, so that the difference between the money in any two adjacent squares (i.e. squares that share a common side) is exactly one euro. So that is exactly what I did.

But then, Oliver, my pet orang-utan, came and took the money that was on one square (8 euro) and Charlie, my pet chimpanzee, came and took the money that was on another one of the squares (22 euro).

Then Gordon, my skint pet gorilla, took all the money that he found on the two main diagonals and blew the lot on a night out with his girlfriend Florence. How much did Gordon spend?

[Semih_Sayginer]

How much did Gordon spend?

too much!

[abextra]

Did Gordon spend 210 euros?

[davis_greatest]

Well done abextra!

Did Gordon spend 210 euros?

Yes he did, abextra! Well done. Gordon spent 210 euros or, in the words of semih, too much.

Since we know that there were squares containing 8 euros and 22 euros, they must have been 14 squares apart, i.e. they must have been in opposite corners (so to get from one to the other, you go 7 squares up/down and 7 squares left/right).

This then fixes all the other squares, so along one diagonal were 8, 10, 12, 14, 16, 18, 20, 22 euros (adding to 120 euros) and along the other diagonal were 15 euros in each square (adding to 8x15 euros = 120 euros also).

So there were 240 euros on the main diagonals - remove the 8 euros and 22 euros taken by naughty Oliver and Charlie, and you get the 210.

Scoreboard to follow...

[davis_greatest]

robert602 in trouble?

robert602, who had a storming start, is now in trouble, only kept off the bottom of the table by new entrant davis_greatest...

HERE IS THE SCOREBOARD AFTER ROUND 27

snookersfun……………………….…..13
Vidas……………………………………….7½
abextra……………………………..…...4½
robert602…………………………………4
davis_greatest…………………..……2

(some rounds may be worth more than one point)
(especially ones won by davis_greatest)

[davis_greatest]

Round 28 - Amazing ages

"Really?" said Megusalah, upon hearing Yonah's age. "That makes you exactly one year younger than I. Amazing!"

"Well," said Yonah, "the even more amazing thing is that if you add up the digits in my age, the sum is exactly divisible by the number of sons I have."

"Oh?" said Megusalah. "That's not that amazing. Because I can say exactly the same. But how many sons do you have?"

"17," said Yonah. "And you?"

"Exactly the same. 17. And happy anniversary, darling."

What is the youngest that Yonah could be?

[snookersfun]

8899 years old?

[davis_greatest]

Another point for snookersfun!

Yes indeed, snookersfun! Building a big lead on the scoreboard.

How did you get it? Didn't cheat and use Excel, I hope?


HERE IS THE SCOREBOARD AFTER ROUND 28

snookersfun……………………….…..14
Vidas……………………………………….7½
abextra……………………………..…...4½
robert602…………………………………4
davis_greatest…………………..……2

[snookersfun]

no excel, no Lagrange... this one was easy

The age of the younger person had to end in 9 otherwise the sum of the numbers would change by one only.
Then I took into account that each 9 turning into a 0 reduces the sum of the older person by 9, thus 2 nines by 18, which can be offset by the gain of one in the hundreds to loose a 17. Two nines at the end need another 16 to reach a sum of 34 (2x17), therfore only 88 or 97 possible, 88 being the lower possibility.

[davis_greatest]

Round 29 - Stand in line!

The questions are coming thick and fast now!

Next year, after the success of the round robin format at the Grand Prix, they decide to have a round robin format at the Crucible.

It starts with all 32 players playing each other once (round robin style).

Show that, after the round robin matches have finished, you will be able to find 6 players and stand them in a line (one behind the other) in such a way that each player in the line has beaten all the players standing behind him.

[davis_greatest]

no excel, no Lagrange... this one was easy

The age of the younger person had to end in 9 otherwise the sum of the numbers would change by one only.
Then I took into account that each 9 turning into a 0 reduces the sum of the older person by 9, thus 2 nines by 18, which can be offset by the gain of one in the hundreds to loose a 17. Two nines at the end need another 16 to reach a sum of 34 (2x17), therfore only 88 or 97 possible, 88 being the lower possibility.

Good - almost perfect. You should also mention though that 7999 is not possible (despite 7 and 9 also adding up to 16, and 79 being lower than 88) because if the number ends in 999 (but not 9999) then adding one decreases the sum by 26.