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Miss Pie thinks of a number then squares it. |
Thag thinks of a different number and squares it. |
 Russ
realises that his number squared is equal to the other two square
numbers added together.What numbers did these people think of? |
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| Arithmetic
| Pythagoras
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Here are the basic solutions assuming they are all thinking of numbers less than 100. Multiples of these solutions are also possible.
| ( 3, 4, 5) | ( 5, 12, 13) | ( 7, 24, 25) | ( 8, 15, 17) |
| ( 9, 40, 41) | (11, 60, 61) | (12, 35, 37) | (13, 84, 85) |
| (16, 63, 65) | (20, 21, 29) | (28, 45, 53) | (33, 56, 65) |
| (36, 77, 85) | (39, 80, 89) | (48, 55, 73) | (65, 72, 97) |
They are all Pythagorean triples.
Here are all of the 104 solutions for numbers up to 100.
| 32 + 42 = 52 42 + 32 = 52 52 + 122 = 132 62 + 82 = 102 72 + 242 = 252 82 + 62 = 102 82 + 152 = 172 92 + 122 = 152 92 + 402 = 412 102 + 242 = 262 112 + 602 = 612 122 + 52 = 132 122 + 92 = 152 122 + 162 = 202 122 + 352 = 372 132 + 842 = 852 142 + 482 = 502 152 + 82 = 172 152 + 202 = 252 152 + 362 = 392 162 + 122 = 202 162 + 302 = 342 162 + 632 = 652 182 + 242 = 302 182 + 802 = 822 202 + 152 = 252 202 + 212 = 292 202 + 482 = 522 212 + 202 = 292 212 + 282 = 352 212 + 722 = 752 242 + 72 = 252 242 + 102 = 262 242 + 182 = 302 242 + 322 = 402 242 + 452 = 512 242 + 702 = 742 252 + 602 = 652 272 + 362 = 452 282 + 212 = 352 282 + 452 = 532 282 + 962 = 1002 302 + 162 = 342 302 + 402 = 502 302 + 722 = 782 322 + 242 = 402 322 + 602 = 682 332 + 442 = 552 332 + 562 = 652 352 + 122 = 372 352 + 842 = 912 362 + 152 = 392 |
362 + 272 = 452 362 + 482 = 602 362 + 772 = 852 392 + 522 = 652 392 + 802 = 892 402 + 92 = 412 402 + 302 = 502 402 + 422 = 582 402 + 752 = 852 422 + 402 = 582 422 + 562 = 702 442 + 332 = 552 452 + 242 = 512 452 + 282 = 532 452 + 602 = 752 482 + 142 = 502 482 + 202 = 522 482 + 362 = 602 482 + 552 = 732 482 + 642 = 802 512 + 682 = 852 522 + 392 = 652 542 + 722 = 902 552 + 482 = 732 562 + 332 = 652 562 + 422 = 702 572 + 762 = 952 602 + 112 = 612 602 + 252 = 652 602 + 322 = 682 602 + 452 = 752 602 + 632 = 872 602 + 802 = 1002 632 + 162 = 652 632 + 602 = 872 642 + 482 = 802 652 + 722 = 972 682 + 512 = 852 702 + 242 = 742 722 + 212 = 752 722 + 302 = 782 722 + 542 = 902 722 + 652 = 972 752 + 402 = 852 762 + 572 = 952 772 + 362 = 852 802 + 182 = 822 802 + 392 = 892 802 + 602 = 1002 842 + 132 = 852 842 + 352 = 912 962 + 282 = 1002 |
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Teacher, do your students have one to one
access to computers? Whether your students each have a TabletPC or share a desktop PC, this activity lends itself to eLearning (Engaged Learning). |
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Here's the URL which will take
them to short quiz about Pythagoras' Theorem.
