快猫短视频

#204 Think of a number

Set by Peter Rowlett

My son鈥檚 book of mathematical magic tricks includes this one:

1. Think of a whole number from 1 to 50.

2. Add 9 and double the result.

3. Multiply by 6 and add 12.

4. Subtract 60.

5. Divide by 12 and subtract 4.

6. Subtract your original number.

7. And the answer is (drumroll鈥�) 1!

Unfortunately, when he is reading, my son sometimes repeats a line and sometimes he skips one. That happened with this trick. He did one of the lines twice and then missed the final instruction to subtract his original number. Yet, by an incredible fluke, he still managed to end up on the number 1.

What number did my son think of?

Solution next week

#203 Multiple magic

Solution

Any magic square will produce a 鈥渕ultiplication鈥� magic square if you raise a constant (k) to the power of each of the original magic square numbers. The smallest k that gives different answers is k = 2. Now, take the original magic square and work out 2^x for each value. The top row becomes 2⁶, 2¹, 2⁸ (64, 2, 256), which makes 2¹⁵ when multiplied together. These numbers can all be halved (32, 1, 128) to get the smallest solution, 2¹² = 4096.