### Brain Teasers

# Madadian Wonks

"I see you have a Madadian stamp there, from the legendary country of MADADIA. Very nice design, especially the picture of Crown Prince Mad Ade eating a kebab. Do you have any more?" asked Norma Leigh-Sober. "No. I did have a 3-wonk, a 9-wonk, a 10-wonk, a 12-wonk, a 13-wonk, and a 14-wonk stamp," replied Rod Wolloper, "But at the airport I used five of them to mail a postcard and a letter. The letter took twice as much postage as the postcard, and that left me with only this one stamp."

What was its value (in wonk)?

What was its value (in wonk)?

### Answer

The total value of the stamps is (3 + 9 + 10 + 12 + 13 + 14) = 61The 5 stamps used at the airport totalled a multiple of 3 wonk, so the remaining stamp must be of value = 1(mod 3). The only stamps meeting this condition are the 10-wonk and the 13-wonk. Assume the 13-wonk stamp remains. Then the total postage was

(3 + 9 + 10 + 12 + 14) = 48 = (16)

But no combination of stamps will make 16, so the 13-wonk must not be the remaining stamp. If 10-wonk stamp remains, the total postage is

(3 + 9 + 12 + 13 + 14) = 51 = (17)

Thus the postcard took (3 + 14) = 17 wonk, the letter took (9 + 12 + 13) = 34 wonk, and the 10-wonk stamp remains.

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