## BEATCALC:  Beat the Calculator!

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 From B. Lee Clay

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### Add sequences of numbers in the 30's

1. Choose a 2-digit number in the 30's. To add all the 30's
from 30 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 3 (+ carry) ` X X _`

#### Example:

1. If the 2-digit number in the 30's selected is 34:
(30 + 31 + 32 + 33 + 34 + 33 + 32 + 31 + 30)
2. Square the 2nd digit of the number:
4 × 4 = 16 (keep carry 1)  ` _ _ 6`
3. No. of terms = 2 × 2nd digit + 1:
2 × 4 + 1 = 9
4. 3 × no. of terms: 3 × 9 + 1 = 28 `  2 8 _`
5. So the sum of the sequence is 286.

See the pattern?

1. If the 2-digit number in the 30's selected is 38:
(30 + 31 + 32 + ... + 38 + 37 + ... 32 + 31 + 30)
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. 3 × no. of terms: 3 × 17 + 6 = 51 + 6 = 57 ` 5 7 _`
5. So the sum of the sequence is 574.