# Can you solve for x?

[$$s$$]   [$$u$$]  [$$r$$]  [$$q$$]  [$$22$$]  [$$r$$] , [$$q$$]  [$$22$$]  [$$p+2k$$]  [$$100-7k$$] ,
[$$q$$]  [$$k$$]  [$$3q$$]  [$$t$$]  [$$100-r$$]  [$$u$$] , [$$21$$]  [$$p+s-k$$]  [$$q$$]  [$$3p+k$$]  [$$23$$] ,
[$$p+s$$]  [$$22$$][$$2p+s$$]  [$$u$$]  [$$s$$]  [$$4s$$]  [$$u$$] , [$$k$$]  [$$r-s+k$$] [$$100-r-s$$] [$$p$$] [$$3q$$][$$12$$],
[$$q$$] [$$100-r$$] [$$u-s$$] [$$23$$] [$$p$$] [$$12$$][$$r$$] [$$t$$].
-x

[  ] lies between 1 and 100(extremes included)
$$p+q+r+s+t+u+k=199$$

$$p,q,r,s,t,u,k$$ are all distinct
$$p,q,s,t,k$$ are odd,
$$r,u$$ even

$$q,t$$ are primes
$$u$$ is largest
$$k$$ is smallest

The multiple $$p\times q\times r\times s\times t\times u\times k$$ does not have any of $$p,q,r,s,t,u$$ or $$k$$.

Hint:

Extremes included can mean that either p,q,r,s,t,u,k ...is 1 or 100...

Hint2:

22 = 'GO'

Hint3:

s 9 || q 19 || u 56 || r 52 || k 1 || t 29 || p 33

• I don’t understand the question. What does -x have to do with the comma-delimited, dot-terminated preceding set of 7 products? Mar 19, 2019 at 15:00
• A further hint might be warranted.
– Rubio
Mar 28, 2019 at 5:20
• @Rubio Added... Mar 29, 2019 at 9:09
• Another hint added Nov 20, 2019 at 17:37
• X is a poet.... Nov 21, 2019 at 18:54

x is:

The poet, William Butler Yeats.

And the puzzle itself is:

A rendering of his poem, The Lake Isle of Innisfree, where each word has been replaced by a number repesenting its value in A1Z26.

I was only able to work this out after Hint 3 gave away the values of s, q, u, r, k, t and p. Plugging these into the mathematics gave:

9-56-52-19-22-52,
19-22-35-93,
19-1-57-29-48-56,
21-41-19-100-23,
42-22-75-56-9-36-56,
1-44-39-33-57-12,
19-48-47-23-33-12-52-29.

Armed with the knowledge from Hint 2:

We know that some of the 22's can be replaced by 'GO'. In A1Z26 'GO' is worth 22 points. Coincidence? I thought not... So I tried calculating the A1Z26 values of common words like 'and' and 'the' and slotted those in where they fitted, noting particularly that 1 would likely be A and 9 I:

I-56-52-and-go-52,
And-go-to-93,
And-a-57-29-48-there,
Of-41-and-100-23,
42-(go)-75-56-I-36-there,
A-44-for-the-57-12,
And-48-47-in-the-12-52-29.

Searching for poem "and go to" led me to The Lake Isle of Innisfree and all numeric values panned out!

I will arise and go now,
And go to Innisfree,
And a small cabin build there,
Nine bean rows will I have there,
A hive for the honey bee,
And live alone in the bee-loud glade.

BOOM! Which all meant that 'x' must be:

Its creator, the poet William Butler Yeats, since this is how a poet's name often appears at the end of their published work, following a short dash. Phew, solved!

I feel like there is more to it than this, as I'm not sure how the X comes into play, but...

Possible values are: $$p=23$$, $$q = 31$$, $$r = 16$$, $$s = 25$$, $$t = 37$$, $$u = 54$$, and $$k = 13$$. Each of the values exist within brackets, so they need to be inclusively between 1 and 100. The operations within the brackets ($$100-7k$$, $$100-r$$, $$r-s+k$$, etc.) all also lie inclusively between 1 and 100. Following the rest of the parameters - $$p+q+r+s+t+u+k \rightarrow 23+31+16+25+37+54+13=199$$, they are all distinct, $$p,q,s,t,k$$ are odd and $$r,u$$ are even, $$q,t$$ are primes, $$u$$ is the largest and $$k$$ is the smallest. Finally, $$p\times q\times r\times s\times t\times u\times k = 23\times 31\times 16\times 25\times 37\times 54\times 13=7407784800$$, which doesn't have any of the numbers within it.

• Solving each set of brackets, you end up with 25 54 16 31 22 16 | 31 22 49 9 | 31 13 93 37 84 54 | 21 37 31 82 23 | 48 22 71 54 25 100 54 | 13 4 59 23 93 12 | 31 84 39 23 23 12 16 37. There are 20 distinct values there. Assigning each distinct value to a letter, I get ABCDEC DEFG DHIJKB LJDMN OEPBAQB HRSNIT DKUNNTCJ. If this is enciphered somehow, it's not a simple cryptogram (or at least not one that quipqiup can solve). Mar 18, 2019 at 21:05
• It looks formatted like a quote to me. Maybe when the cipher is solved, it will be a quote that can be attributed to 'x' which is the name of a person. Mar 20, 2019 at 14:44