All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 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.

 See The Solution Submitted by Ady TZIDON No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 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
NEXT
NEXT
NEXT
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

 Search: Search body:
Forums (0)