# The Sherlock Holmes Problem Solving Challenge - Week 2

**Date:** 14th Oct 2018 @ 12:11pm

One of the most famous gentlemen of the Victorian era, no less than an eminent former cabinet minister, had been the victim of a break-in at his country residence. Fortunately, his safe had remained secure as the burglars had not been able to deduce the four-digit code required to access it.

Look at the numerical sequence below. Can you work out the next two numbers in the sequence that replace the question marks? Once you have done so, multiply those two numbers together in order to ascertain the four-digit safe code.

7688 — 2688 — 768 — 336 — ? — ?

????

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Mr Allen wrote:

Who will be the first to find the answer?

Joseph L wrote:

I keep going over my theory and getting the same answer

Olivia-Martine C wrote:

Please could you write a clue?

Joseph L wrote:

I found out that the two numbers are 76 and 48 because if you look at the first number at all of the numbers the pattern is 7,2,7,3 so I think the two other first numbers are 7 and 4:)

The answer is 3648= 76

x 48

+ 6 0 8

3 0 4 0

3 6 4 8

THANK YOU !!!!!!!!!!!!!!!!!!!!!!! Joseph L

Emily W wrote:

My workings out for this are :

7688

- 2688

5000

So I had an idea to see the difference between 2688 and 768:

2688

- 768

1920

This answer wasn't what I was looking for so I tried again :

336

+768

1104

I tried dividing 1104 by 2 and got this :

0552

2 |1104 =552

552

x 552

114

2760

27600

30474

30474 is not 1104 so te .square root of 1104 = 33.2264954517

33 x 33 = 1104

My answer is 7688 - 2688 - 768 - 336 - 33 - 33 and the safe code is 1104 : )

Joe H wrote:

The code is=1080

Then multiply 7x6x8x8=2688

Then multiply 2x6x8x8=768

Then multiply 7x6x8=336

Then multiply 3x3x6=54

Then multiply 5x4=20

Then multiply 54 by 20= 1080

Jack T wrote:

Sorry Joe I just scrolled through all your guesses and I realised I did the same thing as you

except my apologies

Mr Allen wrote:

Excellent, we have a few different answers!!!

Faye H wrote:

You have to use each digit from the previous number and multiply it so you would do 7 x 6 x 8 x 8 which is 2688 so therefor 3 x 3 x 6 is 54 then you would do 5 x 4 which is 20 so the code is 1080 (54 x 20)

Jack T wrote:

My answer is simple.I did...

7x6x8x8=2688 I could now see what Mr A was doing

Then I did 2x6x8x8=768 straight away I realised a pattern...!

Then I did 7x6x8=336

I did it 3x3x6=54

THEN 5x4=!!!!!!!!!!!!!!!!!20

But it wasn't over yet

It took a while until I found this...

54x20=!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 1080!!!!!!!!!!!! that is the answer

WOW IM SO CONFIDANT

John-Joseph S wrote:

Discussed this all night couldn’t find an answer:(

Mr Allen wrote:

Well done for having a go at it though John-Joseph!

Mr Allen wrote:

Well done to everyone who had a go! And well done to all of the parents tried equally as hard!

The answer:

The numbers are 54 and 20, so the safe code is 1080. To crack the numerical sequence, you need to multiply the digits in each number together to calculate the next number: for instance, 7688 is followed by 2688 because 7 x 6 x 8 x 8 = 2688.

Well done everyone! I'll put the next one on tomorrow...

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