### Whodunni's Dice

Grumpelina, the Great Whodunni’s beautiful assistant, placed a blindfold over the eyes of the famous stage magician. A member of the audience then rolled three dice.

"Multiply the number on the first dice by 2 and add 5,” said Whodunni. “Then multiply the result by 5 and add the number on the second dice. Finally, multiply the result by 10 and add the number on the third dice.”

As he spoke, Grumpelina chalked up the sums on a blackboard which was turned to face the audience so that Whodunni could not have seen it, even if the blindfold had been transparent.

“What do you get?” Whodunni asked.

“Seven hundred and sixty-three,” said Grumpelina.

Whodunni made strange passes in the air. “Then the dice were...”

What? (And how did he do it?)

## 5 comments by 2 or more people

## Samuel Boulby

Dice one is 5. Dice two is 1. Dice three is 3.

He did it with Maths.

02 Nov 2009, 10:22

## Iain

Hmm 5, 1, 3?

I expanded that out to

100x + 250 + 10y + z = 763

100x + 10y + z = 513

bit of a rush though :P

02 Nov 2009, 10:24

## Sebastien Dutrieu

((2a+5)x5+b)x10+c = 763

c has to be 3

b is then 1 or 6

if b = 6, then a = 4.5 which dont work. so b = 1, and a = 5

Simple.

02 Nov 2009, 14:08

## Simon Whitehouse

The equation you get is

763 = 10[5(2a+5)+b]+c

which simplifies to

763 = 100a +250 + 10b + c

So, he took 250 away from the total and then he was left with his answer in the hundreds, tens and units. Like all magicians he used a bit of misdirection to trick the audience from seeing the obvious.

It doesn’t matter what the dice throws are, take away 250 and you are always left with the answer in that order.

02 Nov 2009, 22:14

## Eleanor Lovell

You all got it correct – 5, 1 and 3, although Sam didn’t show his working!

Ian Stewart’s explanation:

If the dice show the numbers a, b, and c, then the calculation produces in turn the numbers

2a + 5

5(2a + 5) + b = 10a + b + 25

10(10a + b + 25) + c = 100a + 10b + c + 250

So Whodunni subtracted 250 from 763 to get 513 – the numbers on the three dice. Subtract 2 from the first digit of the answer, 5 from the second, and leave the third alone.

Magic : )

03 Nov 2009, 10:58

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