Here's the problem:
"the answers below are correct even though the mutiplications are weird. What is the last answer?"
12 23 34 45
x34 x45 x56 x67
---- ----- ----- ----
1013 2003 2663 ??
Can ypu help me out?
Hello, Crossfire!
Answer: .$\displaystyle 3763$The answers below are correct even though the mutiplications are weird.
What is the last answer?
Code:12 23 34 45 x 34 x 45 x 56 x 67 ---- ---- ---- ---- 1013 2003 2663 ????
The first multiplication is in base-5: .$\displaystyle 12_5 \times 34_5\:=\:1013_5$
The second is in base- 6: .$\displaystyle 23_6 \times 45_6\:=\:2003_6$
The third is in base-7: .$\displaystyle 34_7 \times 56_7\:=\:2663_7$
The fourth is in base-8: .$\displaystyle 45_8 \times 67_8\:=\:3763_8$
Hello, Crossfire!
The sets of consecutive numbers got me thinking . . .How did you know that it was in a different base?
. . 12 x 34, 23 x 45, 34 x 56, 45 x 67
More important, I could see that the products were "too big".
. . How can 12 x 34 produce a four-digit number?
. . I knew that this happens when the number base is less than 10.
The first multiplication had the digits 0, 1, 2, 3, 4.
So I suspected a base-5 problem.
I could have been wrong, but it worked out.
The next had a 5, so it couldn't be base-5.
I guessed that it might be base-6 . . . and I was right.
So there was some luck involved, too . . .