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Posts posted by rocdocmac


SpoilerHint: the operation from b to c is the same as from a to b.

Can one solve this mathematically i.e. not by trial and error?
In 1988 my granny was quite a bit older than my grandpa. The difference between the square of their ages was 1988. How old were they?

SpoilerYou'll probably get more than one solution this way, but that is not the answer that I'm looking for!

Replace the question marks below with the missing numbers. The connection is the same between each line of three numbers.
5 ? 575
2 3 ?
? ? 3968

Let's try again ...
SpoilerIf a right triangle, then sum {1/4+1/16+1/64+ ...} = 1/3 inch^2,
or onethird of the area of any other triangle

Spoiler... if it is a right triangle. In other instances the shaded area would equal the area of the original triangle.
Please ignore my answers above  wrong, since there are two cuts in between!
Spoiler 
SpoilerShaded area = infinite sum {1/4 + 1/8 + 1/16 + 1/32 + ... +1/[2^(n+1)]} = 0.5

You got it!
Crypto
Rodent whittling professionally (not really "professionally" as the result seen in the picture!)
Rolling Stones ... (Don't) Play With Fire (added the "don't" to make a meaningful anagram!)


Answer (Thalia got halfway there) ...
SpoilerSchools revoke breathtaking plagiarism > Mikhail Gorbachev, glasnost, perestroika

Unanswered ...
Spoiler3. 632
11. One letter per stable (T E N H O R S E S)

Thanks Dejmar for clearing!





I now understand! Forget my previous stupid questions!

8 hours ago, Thalia said:I'm not quite sure what you are saying. A domino consists of 2 squares. So while there are 56 squares, there's only 28 dominoes. So for example, A2 and A3 together are a single domino.
What I'm trying to say is that, if the layout was made by using 2 complete domino sets, there should be two 00's and two 66's. In the figure there is only one 00 and one 66. So I guess that the given layout makes use of one 66 and one 00 only, but adding duplicate dominoes from a third set, e.g. a third 55.

All cuts should be vertical and in any direction ... I only emphasized that no horizontal cut is allowed, e.g. one could possibly divide a cake with three cuts to yield 8 pieces ... 2 vertical cuts and 1 horizontal cut!
(1) 125251 pieces after 500 cuts (correct)
(2) 3162 cuts gives 500704 pieces (also correct)
(3) Never mind the 3rd answer since I reckon that it must be infinity, although 199999 cuts as a first approximation comes very, very close! However, there will always be a remainder of either 1 or a pretty large number.
Therefore, 2 remains the minimum and maximum piecestocuts ratio. I cannot, though, prove this mathematically (yet)!
I wasn't aware of an entry at "Mathworld"! So, my question should actually have been a straightforward quickie!

Rather change "pizza" to an enormous 2D circle then!
I used pizza as to eliminate any horizontal cut, but it will be a hell of a mess should one really had to cut a pizza into so many pieces!

Thank you TimeLSF! Good one, but ...
Apology for raising this, but there is only one "double 0" and one "double 6" combination directly adjacent next to each other in the grid, although the total of 56 (7x8) matches twice the number of 28 domino pieces in a normal set! The "double 1, 2, 3, 4 and 5" are fine.

Looks like a 7x8 set?

Suppose you have a pizza being cut vertically with one straight cut, you'll be left with two pieces. The ratio of number of pieces to cuts in such an instance will be 2 (a whole number, i.e. no remainder).
If you cut a pizza using two straight vertical cuts, you'll have four pieces left (piecestocut ratio = 2, also a whole number).
Cutting the pizza thrice, the maximum pieces possible is seven (pieces/cuts = 7/3 = 2.3333..., i.e. there is a remainder of 1).
See attached image.
Questions ...
(1) What is the maximum number of pieces that one would get by cutting the pizza 500 times using only straight vertical lines (no horizontal cuts allowed)?
(2) How many cuts should one make to get a maximum of at least 5 million pieces?
(3) The minimum piecetocut ratio with no remainder is exactly 2 as indicate above. What would be the next higher number of cuts, such that the number of resulting pieces divided by the number of cuts has no remainder?

On 6/18/2018 at 1:37 PM, rocdocmac said:9. 31
SpoilerMake that 21!
 1
November Quickie II
in New Logic/Math Puzzles
Posted · Report reply
Excellent
Excellent! I could only do it by trial and error!