## BEATCALC:  Beat the Calculator!

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 From B. Lee Clay

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Dividing Numbers

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### Add sequences of numbers in the 60's

1. Choose a 2-digit number in the 60's. To add all the 60's
from 60 up through this number and down from it:
2. Square the 2nd digit of the number
(keep the carry) `   _ _ X`
3. The number of terms is 2 × the 2nd digit + 1.
4. Multiply the number of terms by 6 (+ carry) `  X X _`

#### Example:

1. If the 2-digit number in the 60's selected is 63:
(60 + 61 + 62 + 63 + 62 + 61 + 60)
2. Square the 2nd digit of the number:
3 × 3 = 9   ` _ _ 9`
3. No. of terms = 2 × 2nd digit + 1:
2 × 3 + 1 = 7
4. 6 × no. of terms: 6 × 7 = 42 `  4 2 _`
5. So the sum of the sequence is 429.

See the pattern?

1. If the 2-digit number in the 60's selected is 68:
(60 + 61 + 62 + ... + 68 + 67 + ... 62 + 61 + 60)
2. Square the 2nd digit of the number:
8 × 8 = 64 (keep carry 6)   `_ _ 4`
3. No. of terms = 2 × 2nd digit + 1:
2 × 8 + 1 = 17
4. 6 × no. of terms: 6 × 17 + 6 = 42 + 1 =
102 + 6 = 108 `  1 0 8 _`
5. So the sum of the sequence is 1084.

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11 January 1999
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