# Help needed for school puzzle

• February 6th 2007, 07:34 PM
Crossfire
Help needed for school puzzle
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?
• February 6th 2007, 08:56 PM
Soroban
Hello, Crossfire!

Quote:

The answers below are correct even though the mutiplications are weird.
Code:

  12    23    34    45 x 34  x 45  x 56  x 67 ----  ----  ----  ---- 1013  2003  2663  ????

Answer: . $3763$

The first multiplication is in base-5: . $12_5 \times 34_5\:=\:1013_5$

The second is in base- 6: . $23_6 \times 45_6\:=\:2003_6$

The third is in base-7: . $34_7 \times 56_7\:=\:2663_7$

The fourth is in base-8: . $45_8 \times 67_8\:=\:3763_8$

• February 12th 2007, 07:18 PM
Crossfire
Thanks
Thanks for the help, but how did you know that it was in a different base?
• February 12th 2007, 10:54 PM
Soroban
Hello, Crossfire!

Quote:

How did you know that it was in a different base?
The sets of consecutive numbers got me thinking . . .
. . 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 . . .