 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Expression Product Exercise (Posted on 2015-09-18) Prove that when all expessions of the form:
+/- √1 +/- √2 +/- ....... +/- √100 are multiplied together, the result is an integer.
As an example, multiplying all expressions of the form: +/- √1 +/- √2 is equivalent to finding the result of this product:
(√1 +√2)( √1 - √2)( - √1 + √2)( - √1 - √2)

**** Extra Challenge: Solve this puzzle without the aid of a computer program.

 No Solution Yet Submitted by K Sengupta No Rating Comments: ( Back to comment list | You must be logged in to post comments.) even UBASIC can get only to 8 in direct calculation | Comment 4 of 5 | (In reply to computer exploration -- far from a proof by Charlie)

5   point 255:dim Term(20)
10   for N=2 to 10
20       Prod=1
25       erase Term()
30       dim Term(N)
40       for I=1 to N
50         Term(I)=sqrt(I)
60       next
70       for F=0 to int(2^N-0.5)
80         Tot=0
90         Bs="":F1=F
100         while F1>0
110           D=F1@2:F1=F1\2
120           Bs=cutspc(str(D))+Bs
130         wend
140         Bs=right("00000000000"+Bs,N)
150         for I=1 to len(Bs)
160           if mid(Bs,I,1)="0" then
170             :Tot=Tot-Term(I)
180           :else
190             :Tot=Tot+Term(I)
200           :endif
210         next
220         Prod=Prod*Tot
230         if N=3 then print using(10,15),Tot
240       next F
250       print N,int(Prod+0.5)
260    next N

2   1
3   64
4   4096
5   23323703841
6   63703464216016403230349121
7   316699666163357097153212433469030615484754548657341071360000
8   122650145964677485280855470979489605455779538020711656443170899516425755208153578926158095907728782598859083391629280893573529600000000

Then there's an overflow.

Rounding was used as there were long strings of 9's after the decimal point in each case.

 Posted by Charlie on 2015-09-20 08:23:36 Please log in:

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