# 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'

• I don’t understand the question. What does -x have to do with the comma-delimited, dot-terminated preceding set of 7 products? – Lawrence Mar 19 at 15:00
• @Lawrence It has some purpose. Any further details would defeat that purpose. – peerless Mar 20 at 6:22
• A further hint might be warranted. – Rubio Mar 28 at 5:20
• @Rubio Added... – peerless Mar 29 at 9:09

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). – GentlePurpleRain Mar 18 at 21:05