Difference between revisions of "2015 AMC 10B Problems/Problem 21"
(→Solution) |
Dubai03wvnsr (talk | contribs) (→Solution) |
||
Line 6: | Line 6: | ||
==Solution== | ==Solution== | ||
63+64+66 = 193. ( ͡° ͜ʖ ͡°) 1+9+3 = 13 | 63+64+66 = 193. ( ͡° ͜ʖ ͡°) 1+9+3 = 13 | ||
− | |||
− | |||
==See Also== | ==See Also== | ||
{{AMC10 box|year=2015|ab=B|num-b=20|num-a=22}} | {{AMC10 box|year=2015|ab=B|num-b=20|num-a=22}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 17:23, 19 April 2015
Problem
Cozy the Cat and Dash the Dog are going up a staircase with a certain number of steps. However, instead of walking up the steps one at a time, both Cozy and Dash jump. Cozy goes two steps up with each jump (though if necessary, he will just jump the last step). Dash goes five steps up with each jump (though if necessary, he will just jump the last steps if there are fewer than steps left). Suppose the Dash takes
fewer jumps than Cozy to reach the top of the staircase. Let
denote the sum of all possible numbers of steps this staircase can have. What is the sum of the digits of
?
Solution
63+64+66 = 193. ( ͡° ͜ʖ ͡°) 1+9+3 = 13
See Also
2015 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.