# Sunday Times Teaser 2766 – Two by Two

### by Graham Smithers

#### Published: 27 September 2015 (link)

Animals board the ark in pairs.

EWE and RAM

HEN and COCK

In fact these are numbers with letters consistently replacing digits; one pair of the numbers being odd, the other pair being even, and both pairs have the same sum. The three digits of the number ARK are consecutive digits in a muddled order. All this information uniquely determines the number NOAH.

What is the number NOAH?

Hi Brian
Your wording omits the useful fact given in the Sunday Times that NOAH is uniquely determined.This makes a manual solution easier because it shows at once that O is zero (O and H can only be differentiated by not allowing H to be a leading zero).
Put another way the fact is a subtle way of forbidding leadihg zeros.
Although I think that a solution with a leading zero would be unsatisfactory it seems that your program specifically excludes leading zeros.
I think that JRC Crabtree’s solution on your other site would be shorter if he had been given this fact.
Best wishes
Tony

Hi Tony,

I take the view that in these sort of puzzles the expectations of ‘no leading zeros’ and unique answers are both implied and don’t hence need to be explicitly stated.

Brian
I agree entirely with your view.
Tony

By using Brian’s Alphametics program I entered the following:
(i) ewe+ram==hen+cock & e%2==0 & m%2==0 & n%2==1 & k%2==1 & -3<a-r<3 & -3<r-k<3 & -3<k-a<3 & ark & noah
(ii) ewe+ram==hen+cock & e%2==1 & m%2==1 & n%2==0 & k%2==0 & -3<a-r<3 & -3<r-k<3 & -3<k-a<3 & ark & noah
These check the even & odd conditions as well as ark being consecutive digits in muddled order.
(i) Gave no solution &
(ii) Gave the unique solution noah = 2074 (ewe+ram=595+873, hen+cock=452+1016, ark=786).
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