perplexus.info :: Numbers : Why? a quickie

Why? a quickie (Posted on 2022-02-06)

Someone asked me to solve it in no time - his alphametic equation using p, q & r
I chose another form, asking you to solve it without any help, no software, no calculators, no pen and paper,
WW+HH+YY=WHY
WHY this choice of letters?
More fun!

No Solution Yet Submitted by Ady TZIDON

Rating: 5.0000 (1 votes)

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Puzzle Solution: Part I

| Comment 1 of 4

The given equation is:

11(w+h+y) = why

Now, w+h+y <= 9+8+7=24

=> 11(w+h+y)<=24*11=264

Then, w=1 or 2

Again 11(w+h+y)=why

=> w+h+y=(my), say where m is the tens digit.

Since w+h<= 9+8=17<20, it follows that m=1, so that: w+h=10..........(i)

Also, 11*(1y)=(why)

=> 110+10y=10*(wh)

=> 10(11+y)=10*(wh)

> y+11=(wh)

when, it follows from (I) that:

w=1 gives: h=9, so that: y=19-11=8 (from (ii))

w=2 gives: h=8, so that: y=28-11=17, a contradiction.

Consequently, (w,h,y)=(1,9,8) is the only possible solution to the puzzle under reference.

Posted by K Sengupta on 2022-02-06 08:04:13

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