I shall make a few assumptions: each word {(w1), (w2), (w3), (w4), and (w5)} are distinctly different; each word represents a number with digits corresponding to each letter of the word.
As there are four partial products, the multiplicand (w3)is a fourdigit number.
As two of the four partial products are the same, i.e., (w1), two of the digits of the multiplicand (w3) are the same.
As (w4) is a oneletter word, (w4) and one of the letters of (w3) each represents a [0].
As each of the differently labelled words are distinctly different, none of the letters of (w3) represents a [1].
Given the product is a multiple of the prime 761, then one or both of the multiplicands is also a multiple of 761.
As the first line is given in quotes, a Google search indicates that the (w1) represents SLEEP.
Assuming that (w3) is, then under the assumptions, and from the hint  'If you suffer from insomnia, (w2) a sleeping PILL', (w3) must be either 3044 or 6088. Yet it could not be 3044 as SLEEP ends in P [3], a digit that could not be a multiple of L [4], while for 6088, SLEEP ends in P [6], a digit that could be a multiple of L [8].
As it is given that there is only one digit missing, with the above assumptions, the "words" are one of the following sets:
(w1) (w2) (w3) (w4) (w5)
SLEEP 234E PILL I S4IL2
SLEEP E54S PILL I S1S5S
SLEEP 359E PILL I S15LS
SLEEP 7292 PILL I 4E7S2
SLEEP 4L4E PILL I 29IL2
SLEEP 9S92 PILL I 5LS52
The hint for (w5) narrows it down to the first, as a SKILT is a portmanteau for kilt and shorts (often with pockets). And the word TAKE fits (w2) for the 'suffer from insomnia' clue.
TAKE 2347
PILL 6088
SLEEP 18776
SLEEP 18776
I 0
SKILT 14082
IKTLL?AP 14288536
The answer to the question "What digit was not used in the above multiplication process?" is [9].
Edited on December 22, 2012, 7:25 am

Posted by Dej Mar
on 20121222 06:23:47 