To solve this, we need to examine more closely Grandpa's words when he says: Two books of International stamps. One book of 75 cent stamps. And I got – 20 cent stamps, 50 cent stamps and also 55 cent stamps. That is it! Knowing that Grandpa spent exactly \$50.00 and bought 13 books, what can we say for sure? If we take his words at face value then we run ...


First Way Second Way Third Way


The completed grid: Step-by-step solution: We start by looking at the We finally filled in a digit, just 80 more to go! Lets look at the bottom box now, Next we look at row 5 again. Now we can make some progress in the middle: We have completed two boxes, we are really getting somewhere! To continue, we look at R3C7. And with that, we have filled ...


(After I saw Rand's solution, it seemed to me that there ought to be a way of streamlining mine a bit. So I've done that. The original version of mine is preserved below in case anyone feels that the improved one is "polluted" by my having seen OP's own answer.) The smallest possible $a+b$ is First of all, notice that Let's Now There is one ...


Solved sudoku (nothing fancy, just plain logical deduction): $$ \begin{array}{c|ccc|ccc|ccc|} & C1 & C2 & C3 \ & C4 & C5 & C6 \ & C7 & C8 & C9 \\ \hline R1 & 3 & 6 & 2 \ & 8 & 5 & 7 \ & 1 & 9 & 4 \\ R2 & 5 & 1 & 7 \ & 2 & 9 & 4 \ & 6 & ...


Probably not the smartest approach but works: (Confession: I did check with computer but only afterwards.) Taken together: The final result is therefore:


Surely must be enough, and also required. After white has two unavoidable captures coming up: on white's next move, the Black can prevent only one of those moves, so the first objective is completed. Continuing from there, white will play next. It threatens black's F-pawn, and also the queen's rook or some other piece in front of it. All those pieces ...


I used integer linear programming (and, sorry, a computer): The solution is unique up to rotation and reflection.


In the following, I've made quite a few assumptions, but to me they all seem somewhat sensible. Looks like there's a chance we can use the first 7 blocks to build a shape with the outline given by OP, or the mirror image of it, which works just as well for the purposes of building a DT gun. To see how this works, let's first improve OP's design by swapping ...


@PaulPanzer made a summary of existing answers here (including some they gave themselves). I want to provide a clearer visualization for each of the existing solutions: Source code for the above program

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