rocdocmac

Excellent

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?

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 ...

Please ignore my answers above - wrong, since there are two cuts in between!

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!)

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).

Answer (Thalia got halfway there) ...

Unanswered ...

Thanks Dejmar for clearing!

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.

Possible solution ...

I now understand! Forget my previous stupid questions!

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.

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!

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 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.

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 (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?