Mind Olympics

A clever, but financially strapped college student discovered that he had spent all of his room and board money on less academic pursuits. Quickly, he telegrammed his dear old parents for cash. However, he was so destitute, he could only afford three words. By an amazingly serendipitous stroke of fortune, he was able to send his request, the total amount needed, and the breakdown in this simple message:
    SEND
    + MORE
    ------
    MONEY
How much did the poor student need, and how much were the two portions for room and board?
Substituting numbers for letters -- solve
Answer:

SEND
+ MORE
------
 MONEY
This cryptogram is amusing in that it spells out a meaningful message and has a unique solution. Deciphering the solution takes some persistent logical reasoning, although inspired guesswork can speed up the process. The obvious initial assumption is that M equals 1. From the fact that SEND #+ MORE is greater than 9,999 we can conclude that S is either 8 or 9, because S + 1 (or 2, if there was a carry from the previous column) is greater than 9. Knowing this yields an upper limit for O; it must be either 0 or 1. Since M is 1, O must be 0. The code now looks like this: 
SEND
+ 10RE
------
 10NEY
The same logic gives us a value for S: if S is 8, then E plus zero is greater than 10 and N is less than 2. (For S to be 8, there must have been a carry) However, N is not less than 2, because all lower values are accounted for. Therefore S is 9. Knowing that there was a carry tells us that E equals N - 1. Looking at the middle two columns we see that EN plus R, plus a possible carry, equals NE. R must therefore be equal 8 or 9, depending upon the carry. Seeing that 9 is taken, R must be 8: Looking at the one's column (D and E), we know there was a carry from this column, so D plus E is greater than 11 (10 and 11 being ruled out because they end with 0 and 1). Furthermore, 8 and 9 are accounted for, so D and E could be at most 6 and 7 in either combination. We also can place a minimum value at 5 for either one, if the other is 7. We also know that E cannot be 7, since it is one less than N. This means D cannot be 5. So E can be either 5 or 6.
Assume that E is 6; D must be greater than 5, and less than 8. Six is taken by E (in our assumption) leaving D equal to 7. But if E is 6, N must be 7. So from the contradiction, we know is not 6, therefore it is 5.
This makes N equal to 6, D equal to 7 and Y equal to 2. The "message" translates to: 
9567
+ 1085
------
 10652
The student needed $10,652. We know this because the method used to solve the problem eliminated the possibility of alternate solutions. So SEND + MORE = MONEY as a monoalphabetic cipher has a unique solution.


It’s the end of another GL competition and you are led into the memorable room where Paladin had his Grey Labyrinth Semaphore clocks. However, this time, the shelf is clean and a pile of lighting equipment is on the floor. A note hangs from the shelf saying “sorry, but I spilled coffee on the shelf and in cleaning it up I completely ruined your light display, so I just disassembled it and left it on the floor” Signed, Skinny. Great you think, it took you a lot of time to setup a nice display message here for the GL competition. Looking at the pile, you realize this can be the final puzzle and ask the contestants if they can put it back the way it was meant to be.

On the floor are an assortment of 3x3 LED boards used for lighting any combination of the 9 bulbs by tying them together with a connector. Meaning that all bulbs are in an off state unless a connector is placed between two of them. The bulbs are 2 inches apart in width and height.
There are 43 connectors of length 2 inches, 6 connectors of a length around 2.8 inches, and 1 connector just under 4.5 inches.  Also, there are 8 LED boards in all. Picking up the boards in no specific order, you find the following information written on the back of them. Note, that on most of these there is no indication of which side is up, so the numbering of the nine bulbs is arbitrary and it may need to be turned to face another way.
1 - Only info is that bulbs 1,2,3,4,6,7,8,9 are ON
2 - Only info is that bulbs 3,4,5,6,9 are ON
3 - Only info is that bulbs 1,2,3,4,5,7,8,9 are ON
4 - Labeled this side up, and bulbs 1,3,4,5,6,7,9 are ON
5 - Labeled this side up, and bulbs 1,2,3,5,7,8,9 are ON
6 - Only info is that bulbs 1,3,4,5,6,8 are ON
7 - Only info is that bulbs 1,2,3,6,7,8,9 are ON
8 - Labeled this side up, and bulbs 1,3,4,5,6,7,9 are ON
You start to say that you don’t know if they can be reassembled without making an assumption, but on the floor you notice labels that were numbered 1 through 8 which used to tell the correct order the boards were placed in. It’s a shame they fell off. But, you only notice seven of them.  As you pick up the boards again, a label marked #1 falls off of a board and lands on the board you temporarily called #3. Unfortunately you are unsure which board it fell off of. Thinking it over, and looking at the label, you exclaim, “Well if you can tell me what the problem was, I’m sure you can now tell me the correct answer as well.”

Image by Courk.
The answer tomorrow. 

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