# Math tapestry puzzle #3

Continuation from Math tapestry puzzle #2

Now things are heating up, it looks like this is slowly becoming bigger. I saw my friend Anna working on her tapestry. She asks me, "Do you like it?"

-- 77 -- -- 06 -- -- 10 --
21 -- AA 51 -- 18 BB -- 58
-- HH -- -- JJ -- -- CC --
-- 76 -- -- 12 -- -- 79 --
17 -- II MM -- 91 KK -- 35
-- 05 -- -- 17 -- -- 40 --
-- GG -- -- LL -- -- DD --
19 -- FF 67 -- 11 EE -- 15
-- 24 -- -- 02 -- -- 07 --


I don't know what happened here, but for sure she's not finished. Can you help her finish her work, given that:

• No variables begin with 6 or 9, nor do they end with 8, or 9.
• AA and CC are prime.
• She has used exactly one number twice.

BONUS QUESTION: In a 6 by 6 puzzle like this, what is the most amount of covered squares allowed and still be able to solve the puzzle?

• K<C<···<E<G is apparent and should not be given. The next four clues each give the value of one variable (although one of them is incorrect) and knowing the value of any variable from the start makes the entire puzzle trivial. The others might also be unnecessary. I recommend removing all of these clues. Mar 17, 2020 at 11:52
• I'm sorry about that... would you like changes? Mar 17, 2020 at 12:05
• That's up to you. The clues just make it too easy. Mar 17, 2020 at 12:11
• I think there are two errors in the puzzle. Specifically, I think that the number rot13(22 fubhyq or 24), and I think that the equation rot13(PP = TT-YY) is wrong. Mar 17, 2020 at 12:42
• IMHO, puzzles should stand alone. For puzzles that people are not familiar with, the rules should be contained within the puzzle itself, and not 2 clicks away. Jun 21, 2020 at 1:28

Step 1:

The first step is to look at some of the adjacent pairs. The largest possible sum is constrained by the $$(05,GG)$$ pair. The largest value for $$GG$$ is $$87$$, making the largest possible sum $$05+87=92$$. The smallest value for $$KK$$ is $$00$$ making the smallest possible sum $$91+00=91$$ via the $$(91,KK)$$ pair. Since we know $$AA$$ is prime and it's in a pair with $$51$$, it must be $$41$$ making the pair sum $$41+51=92$$ (same logic works for $$CC$$).

Step 2:

Now that we know the pair sum is $$92$$, we can find the value of all variables except $$II$$ and $$MM$$ (since they are paired with each other).
$$AA=92-51=41$$
$$BB=92-18=74$$
$$HH=92-76=16$$
$$JJ=92-12=80$$
$$CC=92-79=13$$
$$KK=92-91=01$$
$$GG=92-05=87$$
$$LL=92-17=75$$
$$DD=92-40=52$$
$$FF=92-67=25$$
$$EE=92-11=81$$

Step 3:

We can now fill in any of the 7 completed boxes to get the box sum of $$155$$:
$$06+51+18+JJ=06+51+18+80=155$$
$$79+35+40+KK=79+35+40+01=155$$
$$67+11+02+LL=67+11+02+75=155$$
$$21+77+AA+HH=21+77+41+16=155$$
$$10+58+BB+CC=10+58+74+13=155$$
$$19+24+FF+GG=19+24+25+87=155$$
$$15+07+EE+DD=15+07+81+52=155$$

This lets us find the values for $$II$$ and $$MM$$:
$$II=155-76-17-05=57$$
$$MM=155-12-91-17=35$$
And just to double check $$II+MM=57+35=92$$

The tapestry:

-- 77 -- -- 06 -- -- 10 --
21 -- 41 51 -- 18 77 -- 58
-- 16 -- -- 80 -- -- 13 --
-- 76 -- -- 12 -- -- 79 --
17 -- 57 35 -- 91 01 -- 35
-- 05 -- -- 17 -- -- 40 --
-- 87 -- -- 75 -- -- 52 --
19 -- 25 67 -- 11 81 -- 15
-- 24 -- -- 02 -- -- 07 --

But wait a second, something is not right...

If you were keen eyed you might have spotted two errors in the final tapestry. First, the rules specify that no variables end with 2. However, $$DD$$ is supposed to equal $$52$$. Also, the original rules claim no number is used twice. However, 35 is (once as $$MM$$ and another time in the unfinished tapestry). There's many ways to fix this, so here's one example of a tapestry that follows all the rules with only changing 4 numbers.

-- 77 -- -- 06 -- -- 10 --
21 -- 41 51 -- 18 77 -- 58
-- 16 -- -- 80 -- -- 13 --
-- 76 -- -- 12 -- -- 79 --
17 -- 57 35 -- 91 01 -- 36
-- 05 -- -- 17 -- -- 39 --
-- 87 -- -- 75 -- -- 53 --
19 -- 25 67 -- 11 81 -- 14
-- 24 -- -- 02 -- -- 07 --

• My bad! I forgot that. My brain doesn't always work... Sorry! Jun 21, 2020 at 2:07
• Anyways... do you know the answer to the bonus question? :) Jun 21, 2020 at 2:12