perplexus.info :: Numbers : Last digit counts

Last digit counts (Posted on 2014-07-23)

How many 4-digit numbers are there such that their last digit is either sum or product of the first three?

1. EX: 1258 and 4090 qualify.
2. No leading zeroes.

See The Solution Submitted by Ady TZIDON

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computer solution

Comment 1 of 1

215 satisfy the product requirement.

165 satisfy the sum requirement

Of these, six satisfy both: 1236, 1326, 2136, 2316, 3126, 3216; so the total that satisfy either is 215 + 165 - 6 = 374

_CLIPBOARD$ = ""

FOR a = 1 TO 9

FOR b = 0 TO 9

FOR c = 0 TO 9

prod = a * b * c

sum = a + b + c

IF prod < 10 THEN

prodct = prodct + 1

_CLIPBOARD$ = _CLIPBOARD$ + STR$(a) + STR$(b) + STR$(c) + STR$(prod) + " *" + CHR$(13) + CHR$(10)

END IF

IF sum < 10 THEN

_CLIPBOARD$ = _CLIPBOARD$ + STR$(a) + STR$(b) + STR$(c) + STR$(sum)+" +" + CHR$(13) + CHR$(10)

sumct = sumct + 1

END IF

IF prod < 10 AND sum < 10 AND sum = prod THEN

comboct = comboct + 1: PRINT a; b; c; sum

END IF

PRINT prodct, sumct, comboct

1 0 0 0 *

1 0 0 1 +

1 0 1 0 *

1 0 1 2 +

1 0 2 0 *

1 0 2 3 +

1 0 3 0 *

1 0 3 4 +

1 0 4 0 *

1 0 4 5 +

1 0 5 0 *

1 0 5 6 +

1 0 6 0 *

1 0 6 7 +

1 0 7 0 *

1 0 7 8 +

1 0 8 0 *

1 0 8 9 +

1 0 9 0 *

1 1 0 0 *

1 1 0 2 +

1 1 1 1 *

1 1 1 3 +

1 1 2 2 *

1 1 2 4 +

1 1 3 3 *

1 1 3 5 +

1 1 4 4 *

1 1 4 6 +

1 1 5 5 *

1 1 5 7 +

1 1 6 6 *

1 1 6 8 +

1 1 7 7 *

1 1 7 9 +

1 1 8 8 *

1 1 9 9 *

1 2 0 0 *

1 2 0 3 +

1 2 1 2 *

1 2 1 4 +

1 2 2 4 *

1 2 2 5 +

1 2 3 6 *

1 2 3 6 +

1 2 4 8 *

1 2 4 7 +

1 2 5 8 +

1 2 6 9 +

1 3 0 0 *

1 3 0 4 +

1 3 1 3 *

1 3 1 5 +

1 3 2 6 *

1 3 2 6 +

1 3 3 9 *

1 3 3 7 +

1 3 4 8 +

1 3 5 9 +

1 4 0 0 *

1 4 0 5 +

1 4 1 4 *

1 4 1 6 +

1 4 2 8 *

1 4 2 7 +

1 4 3 8 +

1 4 4 9 +

1 5 0 0 *

1 5 0 6 +

1 5 1 5 *

1 5 1 7 +

1 5 2 8 +

1 5 3 9 +

1 6 0 0 *

1 6 0 7 +

1 6 1 6 *

1 6 1 8 +

1 6 2 9 +

1 7 0 0 *

1 7 0 8 +

1 7 1 7 *

1 7 1 9 +

1 8 0 0 *

1 8 0 9 +

1 8 1 8 *

1 9 0 0 *

1 9 1 9 *

2 0 0 0 *

2 0 0 2 +

2 0 1 0 *

2 0 1 3 +

2 0 2 0 *

2 0 2 4 +

2 0 3 0 *

2 0 3 5 +

2 0 4 0 *

2 0 4 6 +

2 0 5 0 *

2 0 5 7 +

2 0 6 0 *

2 0 6 8 +

2 0 7 0 *

2 0 7 9 +

2 0 8 0 *

2 0 9 0 *

2 1 0 0 *

2 1 0 3 +

2 1 1 2 *

2 1 1 4 +

2 1 2 4 *

2 1 2 5 +

2 1 3 6 *

2 1 3 6 +

2 1 4 8 *

2 1 4 7 +

2 1 5 8 +

2 1 6 9 +

2 2 0 0 *

2 2 0 4 +

2 2 1 4 *

2 2 1 5 +

2 2 2 8 *

2 2 2 6 +

2 2 3 7 +

2 2 4 8 +

2 2 5 9 +

2 3 0 0 *

2 3 0 5 +

2 3 1 6 *

2 3 1 6 +

2 3 2 7 +

2 3 3 8 +

2 3 4 9 +

2 4 0 0 *

2 4 0 6 +

2 4 1 8 *

2 4 1 7 +

2 4 2 8 +

2 4 3 9 +

2 5 0 0 *

2 5 0 7 +

2 5 1 8 +

2 5 2 9 +

2 6 0 0 *

2 6 0 8 +

2 6 1 9 +

2 7 0 0 *

2 7 0 9 +

2 8 0 0 *

2 9 0 0 *

3 0 0 0 *

3 0 0 3 +

3 0 1 0 *

3 0 1 4 +

3 0 2 0 *

3 0 2 5 +

3 0 3 0 *

3 0 3 6 +

3 0 4 0 *

3 0 4 7 +

3 0 5 0 *

3 0 5 8 +

3 0 6 0 *

3 0 6 9 +

3 0 7 0 *

3 0 8 0 *

3 0 9 0 *

3 1 0 0 *

3 1 0 4 +

3 1 1 3 *

3 1 1 5 +

3 1 2 6 *

3 1 2 6 +

3 1 3 9 *

3 1 3 7 +

3 1 4 8 +

3 1 5 9 +

3 2 0 0 *

3 2 0 5 +

3 2 1 6 *

3 2 1 6 +

3 2 2 7 +

3 2 3 8 +

3 2 4 9 +

3 3 0 0 *

3 3 0 6 +

3 3 1 9 *

3 3 1 7 +

3 3 2 8 +

3 3 3 9 +

3 4 0 0 *

3 4 0 7 +

3 4 1 8 +

3 4 2 9 +

3 5 0 0 *

3 5 0 8 +

3 5 1 9 +

3 6 0 0 *

3 6 0 9 +

3 7 0 0 *

3 8 0 0 *

3 9 0 0 *

4 0 0 0 *

4 0 0 4 +

4 0 1 0 *

4 0 1 5 +

4 0 2 0 *

4 0 2 6 +

4 0 3 0 *

4 0 3 7 +

4 0 4 0 *

4 0 4 8 +

4 0 5 0 *

4 0 5 9 +

4 0 6 0 *

4 0 7 0 *

4 0 8 0 *

4 0 9 0 *

4 1 0 0 *

4 1 0 5 +

4 1 1 4 *

4 1 1 6 +

4 1 2 8 *

4 1 2 7 +

4 1 3 8 +

4 1 4 9 +

4 2 0 0 *

4 2 0 6 +

4 2 1 8 *

4 2 1 7 +

4 2 2 8 +

4 2 3 9 +

4 3 0 0 *

4 3 0 7 +

4 3 1 8 +

4 3 2 9 +

4 4 0 0 *

4 4 0 8 +

4 4 1 9 +

4 5 0 0 *

4 5 0 9 +

4 6 0 0 *

4 7 0 0 *

4 8 0 0 *

4 9 0 0 *

5 0 0 0 *

5 0 0 5 +

5 0 1 0 *

5 0 1 6 +

5 0 2 0 *

5 0 2 7 +

5 0 3 0 *

5 0 3 8 +

5 0 4 0 *

5 0 4 9 +

5 0 5 0 *

5 0 6 0 *

5 0 7 0 *

5 0 8 0 *

5 0 9 0 *

5 1 0 0 *

5 1 0 6 +

5 1 1 5 *

5 1 1 7 +

5 1 2 8 +

5 1 3 9 +

5 2 0 0 *

5 2 0 7 +

5 2 1 8 +

5 2 2 9 +

5 3 0 0 *

5 3 0 8 +

5 3 1 9 +

5 4 0 0 *

5 4 0 9 +

5 5 0 0 *

5 6 0 0 *

5 7 0 0 *

5 8 0 0 *

5 9 0 0 *

6 0 0 0 *

6 0 0 6 +

6 0 1 0 *

6 0 1 7 +

6 0 2 0 *

6 0 2 8 +

6 0 3 0 *

6 0 3 9 +

6 0 4 0 *

6 0 5 0 *

6 0 6 0 *

6 0 7 0 *

6 0 8 0 *

6 0 9 0 *

6 1 0 0 *

6 1 0 7 +

6 1 1 6 *

6 1 1 8 +

6 1 2 9 +

6 2 0 0 *

6 2 0 8 +

6 2 1 9 +

6 3 0 0 *

6 3 0 9 +

6 4 0 0 *

6 5 0 0 *

6 6 0 0 *

6 7 0 0 *

6 8 0 0 *

6 9 0 0 *

7 0 0 0 *

7 0 0 7 +

7 0 1 0 *

7 0 1 8 +

7 0 2 0 *

7 0 2 9 +

7 0 3 0 *

7 0 4 0 *

7 0 5 0 *

7 0 6 0 *

7 0 7 0 *

7 0 8 0 *

7 0 9 0 *

7 1 0 0 *

7 1 0 8 +

7 1 1 7 *

7 1 1 9 +

7 2 0 0 *

7 2 0 9 +

7 3 0 0 *

7 4 0 0 *

7 5 0 0 *

7 6 0 0 *

7 7 0 0 *

7 8 0 0 *

7 9 0 0 *

8 0 0 0 *

8 0 0 8 +

8 0 1 0 *

8 0 1 9 +

8 0 2 0 *

8 0 3 0 *

8 0 4 0 *

8 0 5 0 *

8 0 6 0 *

8 0 7 0 *

8 0 8 0 *

8 0 9 0 *

8 1 0 0 *

8 1 0 9 +

8 1 1 8 *

8 2 0 0 *

8 3 0 0 *

8 4 0 0 *

8 5 0 0 *

8 6 0 0 *

8 7 0 0 *

8 8 0 0 *

8 9 0 0 *

9 0 0 0 *

9 0 0 9 +

9 0 1 0 *

9 0 2 0 *

9 0 3 0 *

9 0 4 0 *

9 0 5 0 *

9 0 6 0 *

9 0 7 0 *

9 0 8 0 *

9 0 9 0 *

9 1 0 0 *

9 1 1 9 *

9 2 0 0 *

9 3 0 0 *

9 4 0 0 *

9 5 0 0 *

9 6 0 0 *

9 7 0 0 *

9 8 0 0 *

9 9 0 0 *

Posted by Charlie on 2014-07-23 14:30:25

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