#30 Sticking in a PIN
Sachin tells me that the four-digit PIN that he uses for his credit card has an unusual property. When he enters his PIN into a calculator and squares it, the last four digits of the answer are also his PIN. He tells me that exactly one of the digits in his PIN is a zero, but he won鈥檛 tell me which position it is in.
What is Sachin鈥檚 PIN?
Answer next week
#29 How many strips?
Solution
It is possible to make 15 strips.
To see why, number every position (whether filled or not) in repeated patterns of 1, 2, 3, 1, 2, 3, 1, 2 (next row) 3, 1, 2, 3, 1, 2, 3, 1 etc. In total there are 22 squares labelled with a 鈥�1鈥�.
The way the numbers fall mean that every plank must lie across a 鈥�1鈥�, 鈥�2鈥� and 鈥�3鈥� space horizontally or vertically. All seven holes fall where the 鈥�1鈥� positions are, leaving 15 remaining 1s. This means you can have only 15 strips. There are several ways in which these strips can be cut out.
Quick Quiz #29
1 What is the official chemical name and formula for baking soda?
2 The apparently aberrant brightness of distant type Ia supernovae led astronomers to infer the existence of what mysterious entity in the late 1990s?
3 What is the name given to the supercontinent that made up most of Earth鈥檚 landmass at the beginning of the Neoproterozoic era between 1.1 billion and 750 billion years ago?
4 Jonas Salk鈥檚 name is associated with the discovery of a vaccine in the 1950s for what debilitating disease?
5 Giga, tera, peta, exa鈥� what comes next in the list of orders of 1000?
Answers below
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Quick quiz #29
Answers
1 Sodium hydrogen carbonate, NaHCO3
2 Dark energy. Whatever it is, it is causing the universe鈥檚 expansion to accelerate, meaning distant supernovae are fainter than expected
3 Rodinia
4 Polio
5 Zetta. A zettabyte, for instance, is 1021 or a thousand billion billion bytes