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One digit is missing (Posted on 2012-12-21) Difficulty: 4 of 5
"Oh (w1) it is a gentle thing beloved from pole to pole..."
If you suffer from insomnia, (w2) a sleeping (w3)!
(w4) is one-letter word.
If you want to wear a modern kilt (with pockets) try (w5).
If you multiply (w2) by (w3) your partial products will be w1, w1, w4, w5.
As for the final result, - it is divisible by 761.
What digit was not used in the above multiplication process?

See The Solution Submitted by Ady TZIDON    
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Solution answer | Comment 1 of 3

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 four-digit 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 one-letter 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 7292 PILL I    4E7S2
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   

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 2012-12-22 06:23:47

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