1729
When Srinivasa Ramanujan, the great Indian mathematician, was ill with tuberculosis in a London hospital, his colleague G. H. Hardy went to visit him. Hardy, trying to initiate onversation, said to Ramanujan, "I came here in taxi-cab number 1729. That number seems dull to me which I hope isn't a bad omen."
"Nonsense," replied Ramanujan. "The number isn't dull at all. It's quite interesting. It's the smallest number that can be expressed as the sum of two cubes in two different ways." (Ramanujan recognized that 1729 = 13 + 123 as well as 93 + 103.)
Gauss
About 100 years ago, a young boy (who grew up to be a great mathematician) by the name of Gauss (pronounced "Gowss") was at school when the class got in trouble for being too loud and misbehaving. Their teacher, looking for something to keep them quiet for a while, told her students that she wanted them to "add up all of the numbers from 1 to 100 and put the answer on her desk." She figured that would keep them busy for an hour or so.
About 30 seconds later, the 10-year-old Gauss tossed his slate (small chalkboard) onto the teacher's desk with the answer "5050" written on it and said to her in a snotty tone, "There it is." The teacher, amazed, asked him how he came up with the answer so quickly. So he explained. He noticed that if you add 1 to 100 you get 101, and the same if you add 2 to 99 and so on until you get to 50+51. That's 50 pairs of 101. So he just multiplied 101 by 50 to get 5050.
Curious Facts
111,111,111 x 111,111,111 = 12,345,678,987,654,321
1,741,725 = 17 + 77 + 47 + 17 + 77 + 27 + 57
There are 293 ways to make change for a dollar.
Divide by 7, 11, 13
- Pick any 3-digit whole number. (185)
- Repeat the digits. (185,185)
- Divide by 7 (185,185/7 = 26,455)
- Divide by 11 (26,455/11 = 2405)
- Divide by 13 (2405/13 = 185)
Surprise! You get your original number!
Remainder 3
- Choose any prime number greater than 3. (19)
- Square that number (19 x 19 = 361)
- Add 14 (361 + 14 = 375)
- Divide by 12 (375/12 = 31 with remainder 3)
The remainder will always be 3! (If you add 17 instead of 14, your remainder will always be 6.)
1089
- Pick any 3 digit number. (682)
- Write this number backwards and subtract the smaller number from the other. (682 - 286 = 396)
- Take this answer and again invert it. (693)
- Add your previous "answer" to its inverse (396 + 693 = 1089)
Doing this with any three digit number will either produce 1089 or 0! Even single digits, when written 00x, will work. For example, Try 8. (800 - 008 = 792. Then 297 + 792 = 1089)
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