## BEATCALC:  Beat the Calculator!

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 From B. Lee Clay

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### Add sequences of numbers in the 10's

1. Choose a 2-digit number in the 10's. To add all the 10's from 10 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. The first digits = the number of terms
(+ carry). `nbsp; X X _`

#### Example:

1. If the 2-digit number in the 10's selected is 16:
(10 + 11 + 12 ... 16 + 15 + 14 ... 10)
2. Square the 2nd digit of the number:
6 × 6 = 36 (keep carry 3) `  _ _ 6`
3. No. of terms = 2 × 2nd digit + 1:
2 × 6 + 1 = 13
4. No. of terms (+ carry): 13 + 3 = 16 `  1 6 _`
5. So the sum of the sequence is 166.

See the pattern?

1. If the 2-digit number in the 10's selected is 18:
(10 + 11 + 12 + ... 18 + 17 + 16 + 15 ... 10)
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. No. of terms (+ carry): 17 + 6 = 23 `  2 3 _`
5. So the sum of the sequence is 234.