# 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**?

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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).