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Transcript

The Hotdog Problem!

vs.

Kobayashi

Sonya Thomas

Problems:

How many hotdogs does each person order in round 20? round n?

i cant see this properly how do i zoom out

As shown, Kobayashi starts with 1 hotdog in round 1 and orders 2 more in each coming round, going up by odd #s. Therefore, by round 20, he has ordered 39 hotdogs.

Sonya starts with 2 hotdogs in round 1 and orders 2 more in each coming round, going up by even #s. Therefore, by round 20, she has ordered 40 hotdogs. Sonya orders double the round number of hotdogs (2n), and Kobayashi always orders one less than Sonya.

Round: 1 2 3 4 5 ... 20

Kobayashi: 1 3 5 7 9 ... ?

Sonya: 2 4 6 8 10 ... ?

How many hotdogs, in total, has each person eaten by round 20? round n?

#1- How many hot dogs does each person order in round 20? round n?

#2- Who is ahead after the 20th round? By how much? nth round?

#3- How many hot dogs in total, has each person ate by round 20? round n?

#4- How many hotdogs were on the grill initially?

Kobayashi: 1+3+5+7+. . .39

His Total: 1+4+9+16+. . .400

Sonya: 2+4+6+8+. . .40

Her Total: 2+6+12+20. . .420

Situation:

There is a pattern happening. The sum of the hotdogs that Kobayashi eats after each round is always a perfect square. After the first round, he has eaten 1 (1 squared) hotdog, after the second he has eat 4 (2 squared), then 9 (3 squared), and then 16 (4 squared) and so on. According to this pattern, in the 20th round, Kobayashi should have eaten 400 hotdogs. With Sonya, the pattern is not the same, however in the previous slide it was discovered that in the 20th round, Sonya has eaten 20 hotdogs more than Kobayashi. Therefore, in round 20, the total number of hotdogs eaten by Sonya must be 420; 20 more than Kobayashi. In round n, Kobayashi will have eaten n squared hotdogs in total, and Sonya will have eaten n more hotdogs than Kobayashi.

Who is ahead after round 20? By how much? round n?

How many hotdogs were on the grill initially?

Remember: Sonya ordered 8 hotdogs in round 4, and to beat her, Kobi ordered 9, but they ran out of hotdogs.

Kobi was able go up to 7 hotdogs, and sonya went up t0 8.

Count how many hotdogs they each ate, and then add them together.

Kobi: 1,3,5,7 = 16

Sonya: 2,4,6,8 = 20

So, 16 + 20 = 36. Therefore, the grill initially had 36 hotdogs.

Round: 1 2 3 4

Kobi: 1 3 5 7

Sonya: 2 4 6 8

The table shows how many hotdogs each person orders in each round, and how many more hotdogs Sonya has eaten in total than Kobayashi. In round 1, Sonya ordered 2 hotdogs, and Kobayashi ordered 1, so Sonya is ahead by 1. In round 2, Sonya ordered 4, so she has eaten 6 in total, and Kobayashi ordered 3, so he has eaten 4 in total, making her in the lead by 2 hotdogs.

In round 3, she is ahead by 3 hotdogs. This pattern shows that the # of hotdogs Sonya is ahead by is equal to the round #. Therefore, Sonya is ahead of Kobi by 20 hotdogs in round 20. She will be ahead by n hotdogs in round n.

In an advertisement for paypal, Kobayashi goes to the gas station to purchase some things. While he is paying, Sonya Thomas shows up! Since Kobayashi is the top male for eating Hot Dogs and Sonya Thomas is the top female, these two are enemies! In this video, Kobayashi starts off by ordering 1 hot dog. Sonya, comprehending that he wants a competition, orders 2 hot dogs! Kobayashi then orders 3, and Sonya orders 4, and so on until Sonya orders 8, and kobayashi asks for 10 but there are none left.

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