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## Now Find Another Final Answer?

Last week's Problem was a question asked by Carol Vorderman on Britain's Big Brain Game: “Using simple maths, how can you reach a total of 100 using only six nines?”

The answer "accepted" on the show was "99 / 99 + 99 = 100."

Hint: This option of having multiple answers created a stir amongst people who watched the show.

Solution Commentary: The Andy Merrett Online Blog entry for May 2, 2007 was entitled: "Vorderman’s Big Brain Game has two answers to maths problem: mine is better!"

He reasoned as follows:

"I took this to mean that you had to use six instances of the digit ‘9' and simple mathematics. However, their answer took it that you could string the digits together to make bigger numbers without using maths at all.

Their answer was: 99 / 99 + 99 = 100. Yes, it works, but I have the CORRECT answer:

( 9 * 9 ) + ( 9 + 9 ) + ( 9 / 9 ) = 100
Mine is much more mathematically sound."

BUT what does it mean for an answer to be "much more mathematically sound"? This Blog comment triggered several responses:

Sherwood says (6/9/07): "er dude their answer is way more effecient, how do you work out yours is more mathemathically sound?"

Andy Replies (6/9/07): "I didn’t say mine was more efficient, but nowhere in my maths lessons, if presented with two nines, was there a MATHEMATICAL way to turn that into 99. Just putting the two digits together is NOT maths (ie it doesn’t use addition, subtraction, multiplication, or division. It’s like saying - using simple maths use six nines to make nine hundred and ninty-nine thousand nine hundred and ninty-nine. Oh look: 999,999. Wow. That’s not maths!"

Dreaded Says (10/12/07): “Mine is better” tut tuit - I think half the nation had that answer. And yes the one given in her reply was indeed wrong. There is a distinct difference between 9’s and 90’s and Carol I’d have thought should have known better. Oh well..."

Nicco Says (11/1/07): "Um i think carol vorderman has done nothing wrong here as it is part of a brain game and not a mathematics game, you are only lookin at the problem from a mathematic point of view whereas she has solved the problem logically using more skills, showing she is cleverer than you give her credit for. Anyway your answer is not better and is no more mathematically sound. If anything hers is better because it is simpler. Her answer is a direct answer to the question posed and therefore it is not wrong “dreaded” as she has done nothing wrong, she used simple maths and if you count she only used six 9s. "

Andy Replies (11/1/07): "But Nicco, the questions says “Using simple maths”, not “Using simple logic”. I know Carol Vorderman is clever, but I somehow doubt she writes the questions. I know she only used six nines.

Mike Says (11/10/07): "All very interesting, but if you like a challenge…. Using four 4’s can you construct an equation whose value is 1 Construct one equal to 2, then 3, then 4. Can you do all numbers from 1 to 100?"

David Says (3/26/08): "Can any1 help with this maths problem? whats the missing number? thanx
10.8
5
8
9.33
8
5.67