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# rocdocmac

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## Posts posted by rocdocmac

1. ### November Quickie II

Excellent

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Excellent! I could only do it by trial and error!

2. ### November quickie

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

3. ### November Quickie II

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?

4. ### November quickie

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

5. ### November quickie

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

6. ### Area of an infinitely shaded region

Let's try again ...

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If a right triangle, then sum {1/4+1/16+1/64+ ...} = 1/3 inch^2,

or one-third of the area of any other triangle

7. ### Area of an infinitely shaded region

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... 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!

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8. ### Area of an infinitely shaded region

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Shaded area = infinite sum {1/4 + 1/8 + 1/16 + 1/32 + ... +1/[2^(n+1)]} = 0.5

9. ### Crypto-Anagram #2

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!)

10. ### Crypto-Anagram #2

Here is another cryptogram:

XTWUMG YPNGGBNMC DXTAUFFNTMVBBO

Solve it, then unscramble the letters in the resulting sentence (it is now an anagram) to reveal the name of a rock group and the title of one of their songs (six words altogether).

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This image is a clue to the solved cryptogram ...

11. ### Crypto-anagram

Answer (Thalia got halfway there) ...

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Schools revoke breathtaking plagiarism  ----->  Mikhail Gorbachev, glasnost, perestroika

12. ### 13 BRAIN TEASERS TO MAKE YOU THINK HARD AND TO BOOST YOUR BRAIN POWER

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3. 632

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

13. ### Cutting pizza

Thanks Dejmar for clearing!

14. ### Cutting pizza

Vertical (in any direction) = straight down.

Horizontal as in figure, e.g. a cake. Two vertical cuts give 4 pieces, then the 3rd cut (horizontal ) divides those 4 pieces into two each for a total of 8. Horizontal cuts are therefore excluded.

15. ### Ranks and Files : Dominoes

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Incidentally the domino pieces in the original layout fit in like this ...

All dominoes are actually mirror images of the true dominoes!

16. ### Ranks and Files : Dominoes

23 hours ago, rocdocmac said:

Possible solution ... ﻿

Reveal hidden contents

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Sorry, there is a slight mistake in my image on the left ... one of my dominoes {1+3 @ e5+e6} is upside down, but correct in the right diagram. Here is the correct image.

17. ### Ranks and Files : Dominoes

Possible solution ...

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18. ### Ranks and Files : Dominoes

I now understand! Forget my previous stupid questions!

19. ### Ranks and Files : Dominoes

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 0-0's and two 6-6's. In the figure there is only one 0-0 and one 6-6. So I guess that the given layout makes use of one 6-6 and one 0-0 only, but adding duplicate dominoes from a third set, e.g. a third 5-5.

20. ### Cutting pizza

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  pieces-to-cuts 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 straight-forward quickie!

21. ### Cutting pizza

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!

22. ### Ranks and Files : Dominoes

Thank you Time-LSF! 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.

23. ### Ranks and Files : Dominoes

Looks like a 7x8 set?

24. ### Cutting pizza

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 (pieces-to-cut 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 piece-to-cut 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?

25. ### 20 RIDDLES TO TEST YOUR MATH, IQ AND THINKING SKILLS.

On 6/18/2018 at 1:37 PM, rocdocmac said:

9. 31

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Make that 21!

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