Work Backwards
Problem Solving Strategy
Work Backwards
• A strategy that requires you to change your focus.
• Consider the whole problem in reverse.
• Check by working it forward from your solution to
make sure it is correct.
EXAMPLE:
• Consider planning a vacation to Disneyworld.
Once you find a flight, you need to work
backwards to plan the beginning of your
trip…when do you need to arrive at the airport
and then when must you leave your house to
arrive at the airport at that time, etc.
How many M&M’s ?
After dinner, three friends leaving a
restaurant noticed a bowl of M&M’s on the
front counter.
Eddie took one-third of the M&Ms but returned
four because he had a momentary pang of
guilt.
Cole then took one-fourth of what was left but
returned three for similar reasons.
Adam then took half the remainder but threw
two green ones back.
The bowl had only 17 M&M’s left after the boys
helped themselves. How many M&Ms were
originally in the bowl?
Write down the story steps in order
Begin.
Eddie took 1/3 of the M&Ms.
Eddie returned 4.
Cole took 1/4 of what was left.
Cole returned 3.
Adam took half the remainder.
Adam threw 2 back.
The bowl had 17 M&Ms
left.
Work backwards from the end to the beginning.
• Bowl is full.
• Eddie took 1/3 of the
M&Ms.
• Eddie returned 4.
• Cole took 1/4 of what
was left.
• Cole returned 3.
• Adam took half the
remainder.
• Adam threw 2 back.
• The bowl had 17 M&Ms
left.
48 in the bowl !
32 in the bowl
36 in the bowl
27 in the bowl
30 in the bowl
15 in the bowl
17 in the bowl
Check from beginning to end.
• Bowl is full.
• Eddie took 1/3 of the
M&Ms.
• Eddie returned 4.
• Cole took 1/4 of what
was left.
• Cole returned 3.
• Adam took half the
remainder.
• Adam threw 2 back.
• The bowl had 17 M&Ms
left.
48 in the bowl
48 – 16
32 + 4
36 – 9
27 + 3
30 – 15
15 + 2
17 – it works!
Strategy:
Work Backwards
• Write out the steps in order.
• Work from the end to the
beginning.
• Draw diagrams as needed.
• Perhaps act it out.
• Check from the beginning to the
end.