130 THE FASCINATION OF NUMBERS

When the final result is disclosed, deduct 235 leaving a
balance of 100x+10y-+z. This is the form of all three-digit
integral numbers and the digits of the final number are
therefore the same as the original selections. Thus, if the
numbers 3, 4 and 5 are selected, the respective stages are:
(1) 6; (i) 9; (iv) 52; (v) 56; (vi) 115; (vil) 580; and
580—235 = 345.

EXAMPLE §

This is an example of how simple numerical relationships
can be incorporated into party tricks so dressed up as to
appear to remove the tricks from the realms of pure arith-
metic. Someone is asked to open a book at any page and to
choose any word in any of the first nine lines on the page, to
make a note of that word and to close the book.

He is then told to:

(a) Double the page number and multiply by 5.
(b) Add 25.

(¢) Add the line number and multiply by 10.
(d) Add the number of the word in the line.

(¢) Subtract 250.
(f) Disclose the result.

Thig result will consist of a group of digits in which the
number of the page, the number of the line, and the number
of the word in that line all appear and in the order shown.
Thus, if the second word in the third line of the ninth page
is chosen, we finally obtain the result g32.

If the number of the page be P; of the line be L; and of the
| : word be W; then by stages we have:

BT ..»‘Ww.rdm.mm:w.uwa.ywsmnmpuuw,ymwuiwwammw«w
R D R G 1 { ulnibhin o e A R R MR Rl a8 w-.‘—,.

(a) 2P x 5=10P

(b) 10P+25

(¢) (10P+25+L)10=100P+250-+10L
(d) 100P+250+10L+W

(¢) 100P+10L+W

so that the number ‘PLW’ must result.

et i o1 BRSO 5 AT R gl g g
| i R OEATTL T 11 SO N NI SRR ORIV