# Sunday Times Teaser 2505 – No Title

### by Quentin Fowler

#### Published September 26 2010 (link)

I have taken 15 letters of the alphabet and given each of them a numerical value. They are not all positive, they are not all whole numbers and they are not all different. In fact, four of the letters have the same positive value.

Using these values, I can work out the total value of some words by adding up the values of their letters.

So, ONE has total value 1, TWO has total value 2, and so on up to SEVENTEEN, which has total value 17.

What is the value of NOUGHT?

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(1) Starting with TEN = 10 and FOURTEEN – FOUR = TEEN = 10 shows that E = 0 and T + N = 10

(2) Since E = 0, THIRTEEN – THREE = I + T + N = 10, which shows that I = 0

We can now proceed as follows:

 (3) ___ NINE=9 ___ N=4.5 (4) TEN=10 T=5.5 (5) ONE=1 O=-3.5 (6) FIFTEEN – TEEN = FIF=5 F=2.5 (7) FIVE=5 V=2.5 (8) TWO=2 W=0 (9) SEVEN=7 S=0 (10) SIX=6 X=6 (11) ELEVEN=11 L=4 (12) THREE=3 H+R=-2.5 (13) FOUR=4 U+R=5 (14) EIGHT=8 G+H=2.5

There are two values of 2.5 and we can obtain four by setting U=R=2.5, givingÂ H=-5 and G= 7.5.

So, finally, NOUGHT = 11.5.