If I were to say that:
2 + 2 = 22 2 + q = q2 q + 2 = q2 22 + q2 = q22 2q2 + q = q2q qqq + 22 = qq22 2 x 2 = 22 2 x q = 2q q x 2 = 2q 2q x q = 2q22 q2q x q2 = q22222 qq x qq = q222q
could you then tell me what
2qq2 x qq2 is?
- the '
x' in the above is ordinary mathematical multiplication, the '
+' is addition, and the '
=' is equality.
- each string of
q's is a natural number. Every string is a number, and every number except 0 is a string (including the empty string).
- you do not need every piece of information in the box to determine an answer, though the answer will be consistent with every piece of information in the box.
Since someone got a correct answer, using different reasoning than I did, I'll add my own reasoning below for those who are interested:
First off, the empty string is 1. If some string
xcorresponds to some integer $n$, then
2xcorresponds to $2n$ and
qxcorresponds to $2n + 1$. So
2= $2 \times 1$ = $2$,
q= $2 \times 1 + 1$ = $3$ and so on.
qq2= $2 \times (2 \times 2 + 1) + 1$ = 11, and
2qq2thus = $2 \times 11$ = $22$, the product of which is $242$ = $2 \times (2 \times (2 \times (2 \times (2 \times (2 \times (2 + 1) + 1) + 1))) + 1)$ =