Puzzles with numbers and things

[davis_greatest]

Find a number, that by moving its last digit to the start of the number (e.g. 2349 becomes 9234) will result in an integral multiple (>1) of it.

i.e. abc...de*x=eabc...d

The smallest such number will earn a point. Answers, with explanations (not programs or excel) on the thread.

I think my number is the smallest possible. I'll PM it to you so others can have a go too.

[snookersfun]

Oh well, seems I'm being voted down.

that didn't help, did it? Never mind!

Oh well, seems I'm being voted down.

[davis_greatest]

Not that this was of utmost importance, but I think it's rather the other way round. Sorry for being a know-it-all!

I guess it depends from which end you are looking at the table. The diagram shows the view that the ape breaking off would have.

Lol, us Deutsch-speakers must hold zusammen.

[snookersfun]

pssst, shall I remove my post fast then.....gone-secret now

pst, you weren't supposed to reveal that

It shows the 70 mad reds having to leave... and they move to the positions of the 70 winking blues!

Not that this was of utmost importance, but I think it's rather the other way round. Sorry for being a know-it-all!

[snookersfun]

round 96: moving digits

Find a number, that by moving its last digit to the start of the number (e.g. 2349 becomes 9234) will result in an integral multiple (>1) of it.

i.e. abc...de*x=eabc...d

The smallest such number will earn a point. Answers, with explanations (not programs or excel) on the thread.

[davis_greatest]

Round 95 - picture!

Here is another great picture - thanks abextra for the help with this one too!

It shows the 70 mad reds having to leave... and they move to the positions of the 70 winking blues!

[davis_greatest]

abextra, can we have a picture for the triangle with 20 rows?

[davis_greatest]

I have voted a full point to abextra for the answer and for the pictures... and as my vote is quite important that's settled it. Hehe

SO HERE IS THE SCOREBOARD AFTER ROUND 95

snookersfun.........................47
abextra...............................32
davis_greatest.....................23½
Vidas..................................12½
chasmmi..............................12½
elvaago...............................11½
Sarmu..................................8
robert602.............................7
The Statman.........................5
austrian_girl and her dad.........3½
Semih_Sayginer.....................2½
Snooker Rocks! .....................2½
Ginger_Freak.........................1½
April Madness........................1

[davis_greatest]

Here, courtesy of abextra, is a picture for round 94. I liked it so much that I am trying to decide whether it should be worth a bonus half-point or bonus full point. Would anyone like to vote?

[davis_greatest]

Congratulations elvaago!

I'm going to stick to the trend and say 70!

That is the correct answer!

Here is the general solution if x is the number of balls in the triangle:

When x is divisible by 3, the fewest number of balls that must be moved is x/3.

When x is not divisible by 3, the fewest number of balls that must be moved is (x-1)/3.

So for 15 balls in the triangle, you must move 5 balls.
For 55 balls in the triangle, you must move 18.
For 210 balls in the triangle, you must move 70.


In each case, you must move 3 triangles of reds - one from each corner. When the number of rows is one more than a multiple of 3 (for instance, when the number of rows was 10, which is one more than 9, a multiple of 3), then the triangles moved from each corner are the same size! Otherwise, one triangle moved from a corner is a different size to the other two.

I am going to invite abextra to post here the brilliant diagram she sent me by Private Message earlier today.


SO HERE IS THE SCOREBOARD AFTER ROUND 95

snookersfun.........................47
abextra...............................31
davis_greatest.....................23½
Vidas..................................12½
chasmmi..............................12½
elvaago...............................11½
Sarmu..................................8
robert602.............................7
The Statman.........................5
austrian_girl and her dad.........3½
Semih_Sayginer.....................2½
Snooker Rocks! .....................2½
Ginger_Freak.........................1½
April Madness........................1

ROUND 96 ...

... to follow (I think - once I've thought what to ask).

[abextra]

I'll go for 71.