It’s Wednesday. This Friday looks as distant as the receding memory of last weekend now feels. What to do? Try a quick maths puzzle to jolt the frontal lobes back into action, of course!
Many people have heard, and some are still surprised by, the revelation that ‘7′ is always the answer to the following puzzle:
‘Think of a number. Double it. Now add 14. Now halve the number you get and subtract your original number.’
We’d probably get fewer surprised looks if we rephrased the puzzle as follows:
‘Think of a number. Add seven. Now double that number. Halve the answer. Now subtract your original number.’
The mystery seven was always present in the conundrum, but we can now more easily see where it came from, because we have added it before we double the number, rather than after (when we add double 7 = 14). This principle is illustrated algebraically in a fun Maths-Whizz year 7 game involving magic hankies.
Writing in this week’s Times online, ubiquitous supersymmetry expert and public maths boffin Marcus du Sautoy, discusses a somewhat harder puzzle. We’ve put the puzzle and his explanation below for your mid-week edification. (Of course, if you want more colourful, albeit slightly simpler, fun maths games, we recommend you log into your Maths-Whizz account forthwith):
Think of a three-digit number where the first and last digit differ by 2 or more. Reverse the digits to make a new number, then subtract the smaller of the two numbers from the larger one. Take this new number. Reverse the digits of this new number and add these two new numbers together.
Using my magic mathematical power, I can reveal that your answer is 1,089.
Why is the answer 1089? Well, your 3-digit number is ABC=Ax100+Bx10+C. Reverse the digits and you get CBA=Cx100+Bx10 +A. Let’s assume that A is bigger than C. So ABC-CBA= (A-C)x100+ (C-A)= (A-C) x100- A-C)=(A-C)x99. So you will be left with a number that is a multiple of 99: 198, 297, 394, 495, 594, 693, 792 or 891. Notice that the first and last numbers of each three-digit number add up to 9.
Take one of these three-digit numbers, add to it the reverse of the number and you always get 1089. Eg, 297+792=1,089.
Cool, no? Now back to work/homework/housework/no-work…
