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?

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- Feb 6th 2007, 07:34 PMCrossfireHelp 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? - Feb 6th 2007, 08:56 PMSoroban
Hello, Crossfire!

Quote:

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: .$\displaystyle 45_8 \times 67_8\:=\:3763_8$

- Feb 12th 2007, 07:18 PMCrossfireThanks
Thanks for the help, but how did you know that it was in a different base?

- Feb 12th 2007, 10:54 PMSoroban
Hello, Crossfire!

Quote:

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 . . .