jmc

Question

The letters of the alphabet are given numeric values based on the two conditions below.

∙

Only the numeric values of

- 2,

- 1,

0,

1

and

2

are used.

∙

Starting with A and going through Z, a numeric value is assigned to each letter according to the following pattern:

1, 2, 1, 0, - 1, - 2, - 1, 0, 1, 2, 1, 0, - 1, - 2, - 1, 0, \dots

Two complete cycles of the pattern are shown above. The letter A has a value of

1,

B has a value of

2,

F has a value of

- 2

and Z has a value of

2.

What is the sum of the numeric values of the letters in the word ``numeric''?

Accepted Answer

The cycle has length 8. So the numeric value of a letter is determined by its position within the alphabet, modulo 8. So we determine the positions of all the letters in the word and use them to find the values: n is the 14th letter. 14 8=6, so its value is -2. u is the 21st letter. 21 8=5, so its value is -1. m is the 13th letter. 13 8=5, so its value is -1. e is the 5th letter. 5 8=5, so its value is -1. r is the 18th letter. 18 8=2, so its value is 2. i is the 9th letter. 9 8=1, so its value is 1. c is the 3rd letter. 3 8=3, so its value is 1. The sum is (-2)+(-1)+(-1)+(-1)+2+1+1=-1.