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 Post subject: Maths challenge questions - help needed pleasePosted: Thu Oct 07, 2010 12:28 pm

Joined: Sun Jul 18, 2010 8:02 pm
Posts: 89
1 What is the 100th letter in this endless string of letters?

abbcccddddeeeeeaaaaaabb..

options - a,b,c,d,e

I can see that there is an increase of 1 each time in first 15 letters
then increase of 5 in next...

what are they testing?

2. Each of the letters in the row of boxes represents a number. The sum of any three consecutive numbers in the row is 19. What is the value of I + o + U?

I8WORK4FUN

options - 4, 7, 8, 15, 19

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 Post subject: Re: Maths challenge questions - help needed pleasePosted: Thu Oct 07, 2010 1:54 pm

Joined: Thu Jan 03, 2008 8:26 am
Posts: 1330
Location: Watford, Herts
Minesh wrote:
1 What is the 100th letter in this endless string of letters?

abbcccddddeeeeeaaaaaabb..

options - a,b,c,d,e

Let's count up the letters:

first, 1 a, makes 1

so we were adding ds when we went past 100. A more sophisticated answer would be that the numbers on the right are triangular numbers, with number n being n*(n+1)/2, so the 14th one takes us past 100. We're cycling through 5 letters, so at the 14th step we have the 4th letter, i.e. d (4 is the remainder from dividing 14 by 5).

Minesh wrote:
2. Each of the letters in the row of boxes represents a number. The sum of any three consecutive numbers in the row is 19. What is the value of I + o + U?

I8WORK4FUN

options - 4, 7, 8, 15, 19

First, we notice that for any consecutive four letters, like WORK, we have

W + O + R = 19 = O + R + K

so we have W = K. Applying similar reasoning all along the row, we see that each letter is the same as the one 3 places further on:

I = O = 4 = N
8 = R = F
W = K = U

Because any three consecutive numbers must add to 19, the letters in the last group must equal 7. Thus

I + O + U = 4 + 4 + 7 = 15

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 Post subject: Re: Maths challenge questions - help needed pleasePosted: Thu Oct 07, 2010 2:22 pm

Joined: Sun Jul 18, 2010 8:02 pm
Posts: 89
thanks so much - will have to digest this evening

there will be more - thanks for taking the trouble and sharing your expertise

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