[Guest]

In the sum of the series 50⁰ + 50¹ + 50² + ..... + 50¹⁰¹⁰, it was found that 8 consecutive digits between the 1010th and the 990th terms (counting right to left) can be represented by PIGEOLET.

1) What are these figures?

2) What places they occupy?

[Guest]

In the sum of the series 50⁰ + 50¹ + 50² + ..... + 50¹⁰¹⁰, it was found that 8 consecutive digits between the 1010th and the 990th terms (counting right to left) can be represented by PIGEOLET.

1) What are these figures?

2) What places they occupy?

* This Cryptarithm was created by M. Rose-Innes (Yokoama, Japan) in 1933.

Bonus question:

* M. Pigeolet of (Anvers, Belgium) responded to this Cryptarithm with:

The two words in the name of

ROSE-INNES

from Yokoama are

squares

, while

OR is a prime number

.

What are these numbers?

Edited June 8, 2009 by adiace

[Guest]

DON'T LOOK AT SPOILER IF YOU ARE STILL TRYING TO FIGURE IT OUT

for the original question the answer is PIGEOLET=08163265

ROSE-INNES=9216-53361 (96-231)

I don't get what it means.

[Guest]

DON'T LOOK AT SPOILER IF YOU ARE STILL TRYING TO FIGURE IT OUT

I don't get what it means.

Well u cheated but no problem, you will still have a hell of a coster ride getting to the answer

Each letter is a digit. So in the first one "PIGEOLET" you know that in the 8 letter string, the digit E is repeated but all the other ons are unique.

In the bonus Q, we know that they are squares... that narrows down what is possible.. ROSE has to be between 32^2.. and 99^2. Also note that all 4 digits are different. And we are given the info that OR is a prime (note it can't be anything O and R are unique too.. so 11 is not right).... the more you read into the clues.. the closer you get.

* Wish I had super forum powers.. would remove all googleable strings from the op.. and ur spoiler

Edited June 8, 2009 by adiace

[Guest]

sorry, I did cheat. Thats why I wrote a bold header for others.

I'll try seeing if I can see why them are the answer.

[Guest]

TE=LOE-GIP

56=236-180

[Glycereine]

Starting with ROSE we know that the square must be 4 digits, so the squared number must be between 32 and 99 (31 is 3 digits, 100 is 5).

Since OR must be prime, R cannot be an even number.

This elimates the squares of: 45-54, 64-70, 78-83 and 90-94.

With the remaining squares the following have numbers that repeat themselves: 34,35,38,40,56,58,60,62,63,75,76,77,85,88 and 97.

Further of the remaining squares only the following have the first two digits reversed (OR) as prime.

32 - 1024

33 - 1089

37 - 1369

41 - 1681

42 - 1764

55 - 3025

57 - 3249

59 - 3481

61 - 3721

71 - 5041

84 - 7056

86 - 7396

89 - 7921

96 - 9216

99 - 9801

Now having reduced the possibilities of ROSE to 15, we move on to INNES, noting that the last digit or ROSE must be the 2nd to last digit in INNES, and 0,2,3,7 and 8 are not possibilities.

INNES must be the square of a number between 100 and 316 in order to be 5 digits.

Starting by eliminating any squares that do not have the 2nd and 3rd digits the same or have other digits that are the same, we are left with only:

197 - 38809

231 - 53361

245 - 60025

We note here that in the E place 1 number has a 0 and another a 2, neither of which is allowed based on previously established narrowing of ROSE. Thus INNES must be the square of 231, or 53361.

Knowing now that:

E = 6

I = 5

N = 3

S = 1

We can see that the only solution of the 15 remaining for ROSE that fits with the last two digits 16 is the square of 96, or 9216.

Thus R = 9 and O = 2.

So ROSE-INNES is

9216-53361, the squares of 96 and 231

I haven't had a chance to dig into PIGEOLET much and it hurts my brain anyways...

[Guest]

i don't suppose it had anything to do with Etienne Pigeolet?