aha! : paul scott : many happy returns

#2 98. MANY HAPPY RETURNS

It was my birthday when my friend Peter Grabbit rang me from the Taxation Department. “I have some good news for you,” he confided. “You are going to be sent a refund.”

My thoughts oscillated between a holiday in Hawai'i and an extra bone for Benji the dog.

“The amount,” continued Peter, “is the answer to this sum.” (below right)

Not hearing any jubilant sound of joy, Peter went on, “The number SOW is a perfect square. And that’s my last clue.”

After he rang off, I refleced darkly on the role of ASIO in the Taxation Department, and then went to work on the problem. Normally I hate this type of puzzle, but this one was not difficult.

Did I get to Hawai'i?

As usual, each letter stands for a different digit, and the left hand letter of each word does not stand for zero.

Hints and strategies

Hint 1

Hint 2

Solution

Extensions

              H O W
                    I S
               H  I  S
               S  I  S

HINT 1

Try using W + S + S = S and SOW is a perfect square, to find possible values for S, O, W.

HINT 2

Did you get just two possibilities? Why can one of these be eliminated?

SOLUTION

Running through the possiblilities for SOW with all digits different, we get 169, 196, 256, 289, 324, 361, 529, 576, 625, 729, 784, 841, 961. Since the first digit of the sum cannot be 1, S 1. Now checking ‘W + 2S = S’, we have either W + 2S = S + 10, or W + 2S = S + 20. From the above list we deduce that S = 9, W = 1, O = 6. We now easily deduce that T = 3 and H = 4.

So my refund is $939 – a short holiday in Hawai'i!

EXTENSIONS

There are a large number of puzzles of this sort. The more interesting have a unique solution.

You might look up

http://www.geocities.com/oosterwal/puzzle/cryptq.htm

for example.

#2 98. MANY HAPPY RETURNS
	It was my birthday when my friend Peter Grabbit rang me from the Taxation Department. “I have some good news for you,” he confided. “You are going to be sent a refund.” My thoughts oscillated between a holiday in Hawai'i and an extra bone for Benji the dog. “The amount,” continued Peter, “is the answer to this sum.” (below right) *Not hearing any jubilant sound of joy, Peter went on, “The number SOW* is a perfect square. And that’s my last clue.” After he rang off, I refleced darkly on the role of ASIO in the Taxation Department, and then went to work on the problem. Normally I hate this type of puzzle, but this one was not difficult. Did I get to Hawai'i? As usual, each letter stands for a different digit, and the left hand letter of each word does not stand for zero.**	Hints and strategies Hint 1 Hint 2 Solution Extensions
		H O W I S H I S S I S