#57 Matchstick magic
Your challenge is to move two matchsticks to produce a calculation that gives an odd number. How many solutions can you find?
1-3: well done. 4-6: brilliant. 7-10: amazing. 11: exceptional.
Answer next week
#56 Diffy
While the numbers 1, 3, 9 and 12 give you five Diffy squares (shown below), placing 1, 3, 6, and12 clockwise around the square will give you 10 Diffy squares. You can find them by a combination of wor king backwards and some experimentation. For example, since the final square has 0, 0, 0, 0 at its corners, the one before it must be c, c, c, c (where c is some whole number). To get beyond that, some more trial and error is needed.
Numbers that create a high number of Diffy squares are related to what is known as the tribonacci sequence: 1, 1, 2, 4, 7, 13, 24鈥� Each term is the sum of the previous three (the name is a pun on the more famous Fibonacci sequence in which you add the previous two numbers). Note that the four tribonacci numbers 2, 4, 7, 13 are one higher than our solution 1, 3, 6, 12.
Quick Quiz #49
1 What precious metal, with atomic number 78 and a name derived from the Spanish for 鈥渓ittle silver鈥�, are you likely to find in a car鈥檚 catalytic converter?
2 What does the endocrine system do?
3 How many rooms does Hilbert鈥檚 Grand Hotel have?
4 Dorothy Hodgkin won the 1964 Nobel prize in chemistry for pioneering work using what technique to elucidate biomolecular structures?
5 Some of Hodgkin鈥檚 most influential work involved which product of the islets of Langerhans?
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Quick Quiz #49
Answers
1 Platinum
2 Produce and regulate hormones within the body
3 An infinite number. David Hilbert invented the hotel to expose apparent mathematical paradoxes in accommodating infinite guests
4 X-ray crystallography
5 Insulin; the islets of Langerhans contain the pancreas鈥檚 insulin-making cells